This is not a definitive answer, because I haven't found a firm source to establish when the height standard came into existence, and because the history of army height requirements is turning out to be surprisingly difficult to google.
With this in mind, I'd stick my neck out and suggest that no, the standard if any was probably different when the regiment first formed, and that there probably wasn't a specific standard back in 1506 beyond being, well, tall.
The first hint is the standard itself: 174cm is oddly specific. The unit didn't exist at the time. If we allow that it might have been expressed in (of all things, British) imperial units for some reason, on the basis that measurements in Rome (or Lausanne) might have matched them, then we must also consider how 174cm and 5'8 1/2" are almost exactly the same. That seems too good to be true. Why pick 5'8 1/2" Why not a rounder 5'8" or 5'9" (both numbers turn up when googling it)? That alone suggest me that the standard, if any, wasn't the same when the unit was first put together under Pope Julius II.
(In passing, we can factor in that a typical British WW1 soldier was short enough that they wouldn't have met the criteria to become a Papal Guard. The average height seems to have been 5'5" at the onset of the war, and a 5'7" soldier was apparently rare. So demanding 5'8 1/2" in 1506, to say nothing about the laundry list of other criteria, isn't setting you up for recruitment success.)
The next hint comes from how the Swiss Guard was initially formed. Pope Julius II, a former Bishop of Lausanne, sent a letter to Swiss cantons, asking them to provide him with 200 soldiers. They only supplied 150 for one reason or another. If we assume that they were cooperative (a sensible assumption I think), this can be interpreted in two ways. It could mean they couldn't find enough soldiers (leading one to assume that any volunteer got to go). It could also mean that there weren't enough soldiers that were fit for the job. Question mark, but hold on to that thought.
The leader of this initial force was Kaspar von Silenen. And his wiki page helpfully raises that:
Under Pope Leo X, Kaspar von Silenen's company was one of six Swiss and Grisons mercenary units, totalling 1,800 men, sent to Rimini in the War of Urbino of 1517. They were supposed to help defend the city against the Duke of Urbino until reinforcements could arrive. They were quartered outside the main city walls, in Borgo San Giuliani, because the garrison commander, condottiere Guido Rangoni, was reluctant to let a large mercenary force enter the city. In the evening of 4 August, there were reports of a large enemy force approaching, and Rangoni invited the mercenaries inside, but Kaspar refused due to the late time of the evening, saying his men were already "full of wine". The enemy arrived in the early morning of 5 August and managed to enter the Borgo unnoticed, and killed many of the mercenaries in their sleep. Kaspar also died in this attack.
It unfortunately doesn't say whether this was the Swiss Guard proper, or some other mercenary troops that happened to be Swiss -- I suspect the latter. Still, I'm finding this anecdote about drunk Papal troops hard to square with the "there weren't enough soldiers that were fit for the job" hypothesis that we just looked into. Given the time period, it might be possible to reconcile the two. But seeing how the Pope was recruiting drunkards only a few years later, I'm more inclined to believe that any reasonably fit and honest young man would have worked for the initial batch, and not enough were rounded up.
The last set of hints I came across are from the following two papers on the history of weight and height standards:
They're mostly about the US army, but the two papers offer a few interesting tidbits. You'll hopefully excuse my not remembering which of the two had which bit. Somewhat conflicting hints include:
Roman generals liked tall soldiers, suggesting that there might have been some kinds of standards then and later, with an anecdotal caveat that they preferred muscle over sheer tallness (duh). It's unsourced but it vaguely rings a bell and kind of makes sense.
European monarchs liked to brag about their tall soldiers. Also unsourced, and it doesn't say at what point in time, but I don't find this hard to believe either. If your job is to stand tall next to your monarch -- which is literally part of the Swiss Guard's job description -- it stands to reason that a monarch will prefer that you're tall.
The first precise (or more accurately, vague) fitness for purpose test purportedly arose in July 1775, when the Continental Congress provided that "all able-bodied effective men between 16 and 50 years of age be formed into militia companies". I'm extremely suspicious about this one, and assume it is US related (likely legit) rather than the first ever (yeah right).
Army height (and weight) requirements have been getting refined over time since the Industrial Revolution. I suspect that this too is US related in the article, but I wouldn't be surprised if precise army height and weight requirements appeared and evolved in Europe during the same time period. It is, after all, around that time that Europe became obsessed with scientific measurements.
Put together, I'm finding the evidence somewhat conflicting. The only way to know for sure would be to access the Vatican's archives, assuming they kept a copy of the letters that Julius II sent to the Swiss Cantons. I haven't located any way to access those online.
If I were to guess, I'd suggest that there likely was some kind of standard (it's their job to stand tall at the end of the day, and using height as a recruitment criteria for soldiers wasn't unheard of), but the criteria was "tall" rather than something as specific as 174cm or 5'8 1/2", or perhaps some round number in whichever unit Rome or Lausanne was using at the time. But as already noted, this is pure speculation.
Edit: Mark Johnson chimed in with a helpful comment.
The Roman foot is not the same as the Imperial one. If we assume that there was some kind of express height before the decimal system got introduced, and that Rome still used Roman units when this express height got set (I haven't verified but would be inclined to think it did), then it's interesting to note that 5 pes 14 digitus (= 5.875 pes) is within a few whiskers of 174cm.
This leaves us with two scenarios:
The height limit was introduced after the switch to the decimal system. In this case the answer is clear: the height requirement has changed since Julius II by virtue of it being introduced later.
The height limit was introduced before the switch to the decimal system. In this case it probably was 5 pes 14 digitus at the time of the switch. This being within a few whiskers of 174cm, methinks we can file that under IEE 754 and call it the same.
Assuming the latter scenario, this leaves open the questions of when the height requirement was introduced exactly (was it by Julius II or someone else?) and if it changed over time.