Yo yo yo Ren!
Definitely check with your doctor on the type of sedation/anesthesia they'll be using for the procedure if you're not sure. Protocol differs from doctor to doctor so it's anyone's guess.
Usually it's done under conscious sedation using Fentanyl + Versed, or under MAC anesthesia using propofol. If the doctor said they'll be "putting you asleep" then I'd wager it's the latter, but only the attending physician (and whichever anesthesiologist winds up being there) would know for sure. If you're not a super anxious type then it may not matter, but I'm a worry wart so I always like to know ahead of time so I know what to expect :)
It probably won't be the exact same type of anesthesia used for major surgeries though. That kind requires intubation and it seems doubtful that would be used for LIS, fissurectomy, skin tag removal, or whichever procedure you're having (I may have overlooked it but I didn't see details).
I had just LIS and, like Dawn (who had more done than just LIS if I recall right), was also at the hospital for maybe 3 hours or so. The surgery itself is a small part of that only. The rest is all prep, recovery room waiting, etc. Mine was done under MAC anesthesia with Propofol and went very smoothly (unlike a previous colonoscopy where I only got conscious sedation and woke up midway through

).
I would concur that there's a good chance you'll miss your daughter's school event that evening. I'd hope for the best and expect the worst there, honestly. After I had LIS, I actually felt GREAT for the rest of that day. I didn't feel discomfort or what I could really call post-surgical pain until the next day. But I was definitely tired, and my sphincter was also VERY lax so sometimes ummm "accidents" could happen.
In other words: I think you might be pretty worn out after the procedure, and even if you're not, it's very likely that you'll either be in some pain or just otherwise not be up for the event. It's not really the grogginess that I think will be an issue, more that walking and/or sitting probably won't be terribly comfortable. Better to play it safe and consider it a VERY pleasant surprise if you do wind up making it, IMO.