I’ve never had any problems doing that. bus as noted above, it depends on the brake model and how well it’s bled. Anything with a traditional reservoir on the top (hope, older shimano) will work perfectly even if really badly beld, until you hang it upside down, Avids or anything else with the reservoir at some other unusual angle needs to be perfectly bled to work at all so are perfectly happy upside down.
Other alternatives I’ve used were to put 2 hooks in the ceiling and hang one by its wheels, leaving room for another underneath it. Or I got some L shaped brackets from Claus Ohlsen which held 2 bikes by the top tubes (again, high enough to get 2 more underneath).
Only concern (and this is hypothetical rather than real) is normal seat posts are often open at the top, Reverbs aren’t, I’d worry about water sitting on the seal/valve at the bottom of the post and depositing grit/corrosion (or just corroding the post).