No.
The only way I'd swap Wilson for Carr is if Wilson forced the Seahawks hand. Even then, in a 1-1 trade we'd be getting the short end of the stick. Carr would either have to come with a player, or draft compensation as well.
Carr is a good QB, but Wilson is a tier above him in skill level. Carr is also not the type of QB Pete Carroll looks for in his systems. Derek Carr is a prototypical pocket passer that doesn't have a great deep ball. He thrives on rhythm and timing passes. While not Tom Brady levels of immobile, he's not going to be a threat to run.
Carr is like bizzaro Wilson. He gets rid of the ball a little too fast. He often time bails on routes a little too early. He's very quick to progress to the checkdown. This season he is more aggressive in pushing the ball down the field -- but it's just not his strength as a passer.
I like Carr, but we have the superior QB.