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.