During the Great Depression, was there an increase in the popularity of Communism among the everyday American and if so, was this due to a longing for better living conditions?
Yes, but not enough to really become a significant movement. If you quadruple a miniscule number, you still have a really small number.
In the pantheon of radical leftist movements in the USA, Communism was never really a big player, and the entire revolutionary left was past its prime in the US before Communism became a world player in the wake of the Russian Revolution.
Its tough to find overall objective evidence for this. There were of course individual high-profile people (eg: the Rosenbergs both joined the Young Communist League in the 1930's), but the plural of "anecdote" is not "data".
About the best I know how to do is to look at party membership and vote totals. This is somewhat flawed, due to the American first-past-the-post voting system. Likely many (if not most) Americans with far-left views have always either supported the more left-leaning of the two major parties, or not bothered with electoral politics at all.
That being said, what data I can find seems to back up a couple of points I found made repeatedly:
First, the radical left has a long history in the USA, arguably helping to found a lot of the movements, all of which essentially came crashing to an end with WWI. Most of the larger revolutionary and Socialist organizations came out strongly against the war and the draft associated with it, which ended up being a hugely unpopular stance among the working-class. For many, it was considered an outright treasonous attempt to sabotage the US during wartime, and the perception of these movements as international rather than local likely didn't help matters. Their support seems to have just dropped off a cliff at this point.
For example, some may be surprised to learn that Oklahoma, founded as a state during the Socialist apogee, originally had a very strong agrarian Socialist element in its government. The State's official motto, still listed on its official seals, is "Labor Omnia Vincit" (Labor conquers all). However, after the US instituted a draft for WWI there was a brief quasi "rebellion" from poor tenant farmers, which was used to totally discredit the radical left in the state.
I should note that by and large these farmers were not Communists. It would be more accurate to describe them as Syndacalists, which is a labor movement closer to international Anarchism. Or perhaps you could just call them a group of poor tenant farmers completely alienated from a system that was abusive to them, and leave the arcane political aspects of categorization to the taxonomists.
The second point is that there was in fact a brief recovery of support during early years of the Depression, but it still never made it back up to its pre-WWI heights. The Communist Party didn't even exist as an organization running national candidates in the US during the heady days of 1900's and 1910's. So while they did in fact nearly quintuple their vote total in the first post-crash (1932) election, up to about 100,000 votes, the main Socialist party still got 8 times that (and that total only gave the Socialists 2.2% of the total vote. In 1924 with no handy depression around, and their candidate in jail, they had gotten 3.4%).