Yes, but my understanding is that they were written following Paul's example.
For instance, I once asked a teacher if the Gospels, written by Jews for a the followers of a Jewish rabbi, were originally written in Aramaic. With the possible exception of Luke, we are pretty certain that the original versions were written in Greek, and not Hebrew or Aramaic, because the Gospel writers were following the convection set by Paul. Christianity did not have any texts (other than the traditional Jewish ones) before Paul, and his actions prompted other people to write down their oral history of Jesus.
The fact fact that Paul chose to write in Greek, is itself interesting, and reflective of the content of his reformed message; that it was one meant for the world, and not just the Jews (which it can certainly be argued was not the case of Jesus's original teachings).
The earliest Gospel (Mark) is thought to have been written about the same time as the last letters of Paul, so this is plausible. But even if they were responding to Paul, they may have been responding against him, not responding to imitate him.
All that is speculation, but we know from reading them that the Gospels have a different focus than the letters.
Luke was traditionally thought to be a Gentile &, if so, wouldn't speak Aramaic. Some of Luke is copied from Matthew, & some from Q, so it's pretty certain it was written in Greek.
My take on some historical religious/social/political movements:
The best strategy for complex social movements is not honest rationality, because rational, practical approaches don't generate enthusiasm. A radical social movement needs one charismatic radical who enunciates appealing, impractical ideas, and another figure who can appropriate all of the energy and devotion generated by the first figure's idealism, yet not be held to their impractical ideals. It's a two-step process that is almost necessary, to protect the pretty ideals that generate popular enthusiasm from the grit and grease of institution and government. Someone needs to do a bait-and-switch. Either the original vision must be appropriated and bent to a different purpose by someone practical, or the original visionary must be dishonest or self-deceiving.
There are exceptions to this pattern that, I think, prove the rule when you look at them more closely:
And then there are just exceptions:
One interesting aspect of the pattern is its hysteresis. Once idealism has been successfully co-opted, the resulting organization can continue to siphon that credibility indefinitely, while dismissing its more radical demands.