Sure, go for it.
With my 'rules hat' on, I'll quote the help centre's guide to what's on-topic
Science Fiction & Fantasy Stack Exchange is for questions targeted towards science fiction and fantasy enthusiasts. This includes questions about:
- Plot, character, or setting explanations
- Historical or societal context of a work
- Behind-the-scenes and fandom information
- Story identification
- Franchise/series reading or viewing order
A question about the behind-the-scenes antics of the Star Trek cast definitely qualifies under the "Behind-the-scenes and fandom information" bullet-point.
Now with my 'reasonable hat' on, I'll say why I think this should
What we have here, on this site, is a community of science fiction and fantasy experts. A question like the one you suggest, while not being in-universe, is still going to be answerable by people who are Star Trek fanatics (looking at you, @Praxis) - it seems perfect for our site. (Admittedly the same argument could be applied to questions which are not on-topic, such as list and recommendation questions, but they fall under the "primarily opinion-based" bracket.) Provided your question isn't:
- too broad
- primarily opinion-based
- unclear what you're asking
(which it isn't), then hell, go for it!
: once you've asked your question, I'll upvote it :-)