Mostly no. However, there are a few times they can be uncomfortable.
When you first have the braces placed, they will irritate the lip and cheek for the first few days until you are more used to them. The orthodontist will provide soft wax to cover the braces so you can adjust a little at at time. The day after placement will be the most difficult. Every day after will be better. Which ever side of your face is on the pillow when you sleep will be the most sore.
The teeth will also be sore for the first few days. It feels like having a seed or food stuck between your teeth that you can’t take out. More annoying than sore.
Taking some Tylenol, Motrin, etc. before have braces placed or an adjustment will be helpful. Also, chewing some gum, or a chew wafer for the half hour after the adjustment will make the teeth less sore.