Is it normal for a hat brim to droop after curing?

Almost certainly the supports and the flexing while you were snipping them off, not the cure. Over-curing on a mini this size mostly causes brittleness and a slightly chalky or shiny finish, it doesn't really warp a brim after it's already solid on the plate. The droop you're describing usally shows up when the part spent time under tension in the tank, or when the supports under that thin edge got stressed during removal. If supports were tucked right under the brim and you had to wiggle the figure to get them off, that's your culprit. A hair of droop on a floppy hat honestly reads as intentional on a scarecrow, so I'd prime it and see how it looks painted before reprinting anything. For thin bits like the scythe handle, the bending while snipping is normal and mostly springs back because the resin is still slightly flexible at that thickness. The trick is to not cut against the part. Hold the support and pull, or snip from the contact point side rather than levering the part itself. If something does stay bent, a quick warm water soak or a few seconds with a hair dryer softens it enough to gently flex true, then it holds shape once cool. Don't dunk the whole mini, just work the bent bit.

One thing to check on future prints: orientation. Tilted hats and brims print better at an angle with the underside supported along the curve, since flat thin plates parallel to the plate tend to cup or sag slightly. For this guy though, a jack-o'-lantern headed scarecrow with a droopy hat is the look. Reprint only if the curve bugs you after priming.

Agree it's the snipping. I ruined a wizard's wide collar the same way, flexed it going at the tips and it stayed cupped. Since then I pull supports off in one pass by grabbing the bar and rolling them, barely touch the model. Even double cure time won't bend cured resin, it just makes it snap instead of flex, so you'd have heard a crack before you'd see a droop. On the scythe, try twisting the snips so the blade meets the tip flat instead of levering sideways, that stopped the white stress marks on my thin stuff.

Been doing this since we were curing minis in a shoebox with a UV nail lamp and hoping for the best, and I can tell you a floppy brim on a scarecrow is a feature, not a bug. If it still bugs you after paint, soak the brim in hot tap water for a bit and coax it back by hand, that trick is older than most of the printers on this forum.

I'd print the next one and compare before touching this guy. When I over cured a batch of minis by forgetting them in the cure station overnight, the only change I noticed was they snapped easier when I dropped one, nothing moved or warped. So if your brim looked flat on the plate, something bent it after. Mine was a contact point I didn't see, left a little nub and tugged the edge when I twisted it off. Now I hold the model steady with the flush cutters flat against the base and it made a big difference.