I never drop when it is an actual game or other "event", but for daily type practices, then yes, I do. Regularly.
I can remember when I started dropping off my son at his karate class... I never had really had a reason not to stay and watch (the classes were only 45 minutes) until my daughter started gymnastics. Her gymnastics class started 15 minutes after his karate class (and was right around the corner a street over). He was in 4th grade, she was in 1st. I dropped him off (watched him go into the building) then drove daughter to gymnastics. I stayed with her for the first 20 minutes of her class, then left and drove back around the block to pick up son. Then returned WITH him to pick her up as her class was getting out a few minutes after that.
Once I started doing that, it occurred to me that I could be getting a lot of stuff done (grocery shopping!) when he was in class 2x a week. So, when she stopped gymnastics, I started dropping him off and going to the grocery store and then coming back to get him with a couple minutes to spare before his class ended. As he got older (and the classes sometimes ran later and later--beyond the "scheduled" time...) I started timing my grocery trips so that I picked him up "late" (so that I was certain he was ready to go so my frozen stuff stayed that way for the trip home).
Now, they both are in karate classes. Not the SAME class, though, yet. He is a 2nd degree black belt and is 14 years old in 9th grade. She is 6th grade, and 11 years old. They have been attending the same karate school for years and are VERY comfortable there. In fact, everyone there knew her before she was a student, by virtue of the many years of her sitting watching her brother. The instructors are fine with them hanging out before/after class until I get there. They play on their ipods or talk quietly with friends (inside the training room--while other classes are going on) or read a book. Sometimes they assist in other classes (of lower ranked students). If it is not a chaotic time (after school pick-up hours are pretty hairy sometimes with all the parents getting their kids between 5 and 6), sometimes they hang out in the "office" and play pranks on some of the younger instructors. My daughter likes to adjust the pneumatic chair so that they sit down lower than they are expecting. Sometimes they write sticky notes and stick them to someone's back unbeknownst to them. It is all in good fun and the instructors are part of it. My kids are well behaved and respectful, and they know when to stop.
The school has my cell phone number, as do both my kids. And if something were to happen, I'm only 5 minutes away at the grocery store or Target, or Bed Bath & Beyond, or Petsmart.
If my children were not comfortable with this arrangement, then I wouldn't do it. Daughter usually has a book to read for when her class is over and her brother's class is going on. Son is usually on his ipod during sister's class. He is often comparing gaming info with some of the older teens. Most of the people at the school (both employees and students) are the same ones who have been there the entire time we have been there. My son started karate at 5 1/2 years old at a different branch of the same school. When he was in 3rd grade, he switched to this school, and one of the instructors he liked from his original school also made the switch to this school (totally coincidental). Many of the non-master instructors switch around between the various branches... and son knows LOTS of them. It is like a 2nd home to our kids as far as their comfort level. And they do NOT go outside the building when I am not there.
Not a big deal at all for us.
I would have been comfortable dropping him off at an even earlier age if it were necessary. Her, probably not so much.
The only times they get annoyed about being there when I am not is when one of them wants to go WITH me to run errands because they want something from Target or want to shop for shoes or something. LOL