Our school is very, very heavy on parent participating (it's required), so I see parents in and out of the classrooms all day. Last year I never ONCE stopped to check in with the office, sign the visitor/classroom helper log, and get a badge. I literally kept a badge in my car because I was in the classrom *SO* much! DD's teacher needed the help and being a SAHM with a child who just started kindy, I was GLAD to be in there so much!
With that being said, this year is a whole different ballgame. DD2 started kindy this year and I needed to take her glasses to her and did it during her recess break. Of course she started in with the "Mommy, don't leave" and it became a MAJOR scene. Right about that time the secretary walked up to me and during the convo she said, "That's what we are here for! Just drop them off in the office and we will get them to her." She said it in a nice way and was trying to be helpful (I'm sure she could see the distress on my face!) and I had to laugh because I told her that it had never occurred to me to take something to the office!!
I guess to answer your question, I would be very upset if they told me I wasn't allowed to just pop in to my child's class, but I can understand the disruption. I joke around and say that every time I go into one of my children's class I feel like Norm from Cheers! All the kids flock to me and immediately want to show me what they are working on. It's a Montessori school, so they have a 2.5 hour work period where they are up and moving around, so even though there is that initial bum-rush to the Mommy in the classroom, they quickly settle back in to what they are doing when I say, "Show me what you're working on!"
I think you should be able to pop in the classroom anytime you want. Is it possible to be a classroom volunteer a couple days a week?