Comedy can be a great emotional counterbalance to good drama.
What makes it difficult is that Galaxy Quest was such a good comedy yet with good dramatic content (Data's laughing fits in Generations were just slapstick).
If Galaxy Quest had been slapstick then humor in the new film would be fine in the sense of "The Voyage Home" but not now.
Even the Bond franchise had to reevaluate what they were doing after Austin Powers. As one of the Bond crew said in an interview "there is not a lot of difference between ***** Galore and Alotta ***ina".
Red shirts dieing with an obvious set up, Kirk pulling off his shirt as a wink to the series etc will make the film far more like Galaxy Quest 2 than Star trek 11
Perhaps that would not be a bad thing, Galaxy Quest was better than any recent Trek film.