Both my DD's had TT and both were snipped on Day 3.
DD1 couldn't stay latched on at all, and it took 48 hours before a midwife suggested she might have TT - consultant snipped the next day. He took her away, but was back within 2 minutes and she latched on straight away - I cried!! :) Fed her until 17 months.
DD2 (4 months old) - we were more aware this time and asked the midwife to check her straight after my EMCS (for breech). She could latch on, but was really "clicky". Had to wait a couple of days for the consultant but again all done within a couple of minutes and then she latched on correctly.
Neither of my DD's were crying when he brought them back, so can't have been too painful!!
After trying to breastfeed DD1 for 2 days with absolutely no luck I was desperate to try anyway and was pretty much begging the consultant to do it (not that I needed to, but I had to consent to be being done).
As others have pointed out, it can lead to speech problems if not done and would need GA to have it done later. It is so quick and IME the baby doesn't seem bothered by it. The only downside I believe is that there is a tiny risk of infection, but I remember it being tiny (can't remember exactly).
Personally I would say go for it whilst its an easy thing to do.
Good luck