Very good question, I bet they would have no problem with me doing that!
It's really only a few seconds to fill out the form. I could also probably see if I could just drop off his bag on the counter and they could put his stuff where it belongs.
I could definitely do a better job communicating with them about it, I always feel so rushed in the morning and then at pick up the main girl's shift has already ended and there's a different girl. Just another reason I miss our old daycare