After watching the first episode I can absolutely recommend that any fan of Star Trek give this show a shot. It's clear that the show creators have a connection to this universe and are careful to play with the common themes of any Star Trek episode, while poking fun at the more eccentric qualities of what makes Star Trek great.
Personally, I found the comedy to be very funny. The animation style you'll recognize from Rick and Morty which lends itself to the setting. One criticism is the voice acting can be frantic and loud. If you are familiar with cartoons this won't bother you, but perhaps Star Trek fans that don't watch animations will find that annoying. But thats a nit-pick.
With so many easter eggs, inside jokes and small references; any Treky should find something to enjoy here.
If you are a Star Trek fan that is somehow offended by comedy, chill out.