It's tricky
(but probably no)
The maps you see come out of 19th and 20th century historiography, during the rise of nationalist agendas. This is further complicated by the Internet echo chamber.
There's some indication that the Franks had control over Pannonia (present-day Austria towards the end of Charlemagne's reign, and had the early Moravian duchies as a dependent state, but Bohemia is a bit of a historical donut hole in the early 9th century. And that's a clue.
The Franks appear to have claimed a protectorate over Bohemia, but there's no indication whether they had any control or even a presence there.
A lot of the history of Bohemia prior to the mid-9th century is mostly legendary.
Before Charlemagne appeared on the scene, the area was dominated by the Avars, a mostly-nomadic people whose control consisted of suddenly appearing as unwanted houseguests, stealing the livestock, and sleeping with the local women.
According to the Chronicle of Fredegar, a Frankish merchant named Samo, united several Slavic tribes in the 7th century and defended them against attacks from the Franks and Avars, but his empire fell apart upon his death. The Avar khagan received a major defeat in 626 at the First Siege of Constantinople and this fits within the timeline of Samo's rise.
In 796, Charlemagne defeated the Avars in what is present-day Austria.
(The khanate of Bulgaria absorbed the Avars in the East).
The Franks had help from the Slavs in the area, so parts of the Avar Marches the Franks set up were put under the control of local Slavic princes. The Duchy of Moravia appears in 822 with a record of tribute by Duke Mojmir to Louis the Pious. This later developed into the Empire of Great Moravia.
The first historical ruler of Bohemia is the Přemyslid ruler Bořivoj I. Initially under the suzerainty of Svatopluk I of Great Moravia, he became independent as Great Moravia fell apart upon the appearance of the Magyars. Bořivoj was later given a legendary pedigree of seven princes connecting him back to Přemysl himself, which may have originated from back-interpreting a collection of frescoes in a 12th-century church in Znojmo.
Not so much
The biggest clue we have is that the christanization of Bohemia didn't begin until after Bořivoj took control of Bohemia in about 870. The christanization of the (western) Avars began with their submission to Charlemagne in 796, and it's claimed the Moravians were baptized en masse in 831.
And to take your question literally, the answer is "almost certainly not". There wasn't enough time, and there aren't any records when there are records about nearby areas. Charlemagne conquered the Avars in 796 and died in 814; Mojmir's tribute of 822 is the first mention of Moravia; an 805 pacification raid into Bohemia in the Royal Frankish Annals is the first mention of the Bohemians.
Eodem anno misit exercitum suum cum filio suo Carlo in terram Sclavorum, qui vocantur Beheimi. *Qui omnem illorum patriam depopulatus ducem eorum nomine Lechonem occidit; et inde regressus in Vosego silva ad imperatorem venit in loco, qui dicitur Camp.
"In the same year he sent his army with his son Charles into the land of the Slavs, who are called Beheim. Who, having despoiled all their country, killed their leader named Lechon; and returning from thence to the forest of Vosego, he came to the emperor in a place called Camp."
but this is all we hear of the Franks until their mention by the Bavarian Geographer c.830 in a list of Central and Eastern European tribes.
