I can see Tarantino doing something like that. "A Piece of the Action" is a nicely over-the-top comedy. (Vic Tayback is in it. VIC TAYBACK. Mel's Diner's Vic Tayback.) The episode happened in part because the late, great Trek producer Gene L. Coon wanted to do more comedy on the show, since "The Trouble With Tribbles" had come out so well (and years before, in his proposal for Star Trek, creator Gene Roddenberry had written the one-line episode concept "President Capone"). Tarantino being funny with Star Trek is something that almost happened...and might still happen, as I've heard it's yet to be officially canceled.
It's nice to hear more about the concept, because almost all I'd heard about it had been, literally, jokes. Easy jokes, more to the point, based on just dumping certain Tarantino tropes into Star Trek and assuming that's automatically funny. Kirk and Spock talking about food would not sound at all like Vincent and Jules talking about McDonald's. (I'm certain there is no scene in the script of Kirk and Spock talking about food.) It would have been an interesting challenge for Tarantino, plus he wanted to do it as an R-rated film (though a PG-13 or even PG Tarantino is also interesting to think about), and I'll be honest, I kind of want to see it. Star Trek is deeply flexible as a storytelling device. Why not this?