I did this with my daughter (also 3) and really only had to do it for 2 days before she started going on the potty more than in her pants (we just cold-turkeyed the diapers except for bed-time and stuck in her in underpants - the actual amount of dirty laundry produced was minimal). Another day or 2 after that and she was going pee in the potty every time (poop is another story, we are still working on that). We would put a pull-up on her when going out but she's been great about keeping them dry. She has preschool today and this morning she actually asked me if she needed to wear a pull-up to school. I asked if she wanted to go without one this time and she said yes, so I said okay, but you will need to remember to use the potty if you have to. We've been at it almost 3 weeks and this will be our first trip out of the house just in underpants. She's been great about going potty on her little potty but is still not wanting to use the big potty, so we would just have her go pee before leaving the house and have a pull-up on her just in case, since we still need to warm her up to the idea of actually using a big potty in a public restroom (and maybe she would also be so distracted being out she could be more prone to an accident).
I would see at what point he is consistently using the potty and not having accidents, how long he stays dry for, then maybe try taking him out if he goes pee first. It will depend on how much he's been drinking and how long you think he can "hold it" before he will need to go again (DD can hold sometimes 4 or 5 hours!). For some kids, pull-ups are too much like diapers and don't really help at all, but DD has been doing well and seems to understand that she is not to pee in them either if she can help it - they are "just in case".