I'm sure your ds is fine, but one characteristic of ADHD is hyperfocusing on things that interest them. Video games, spongebob - ADHD kids love these things.
I understand that, but that applies to all kids(and adults) as well. I didn't fully explain all the details, but basically he didn't have any other symptoms other than he didn't pay attention sometimes. "Sometimes" was usually circle time. . .so I observed. I clocked it. . .47 minutes sitting on a rug. Roughly 3/4 of that time was spent explaining and counting by 5s to 100. Well, my son already knew how to do that. I was not surprised that he started to tune it out, as well as about 5 other kids that were engaged in various distractive behavior. The teacher was a 1st year teacher and some of her methods were a little off for the grade she was teaching (she would assign roughly an hours worth of homework every night). My son was beginning to dislike school.

She had talked to other parents as well, and they were coming to me because they knew I had taught. They were confused because the kindergarten teacher had never brought these things up. She was just finishing up her PhD. She was very good. . .I would say an expert for that grade level. She ran a fairly loose classroom and ascribed more to the Montessori type self guided learning. It was an adjustment for these kids to move into a rigidly structured room, where the teacher was unrealistically expecting perfect behavior. She hadn't done any assessments yet and was teaching to a level below where most of her students were at. I think that most of us that have ever taught know that is a recipe for disaster. Especially with 6-7 year olds!
Anyhoo. . .I am all for helping kids succeed, doing assessments early, getting to the bottom of any potential problems and developing a plan of appropriate intervention. BUT I also think it's a disservice to kids to automatically label them ADD/ADHD, when in fact, the problem may not lay with them at all. The big picture needs to be taken into account. Just as an example, my last year of teaching 4th grade, I had a boy that had some really disruptive behavior right off the bat. Early assessment reveled that he was only reading at mid 1st grade level. I pulled him aside and told him what I knew. I was going to have him go with our sped ed liaison for some help with that. I would never call on him to read aloud in class (social suicide for him), and that I thought he was a smart kid. . .one of my brightest kids in math. I suspected that he might be dyslexic and he was mildly. I also told him that doesn't give him a pass or mean he's stupid. It just means that his brain works a little bit differently and he was going to have to work harder because of it. Just knowing that I wasn't going to call on him to read aloud completely eliminated his disruptive behavior. he got the help he needed and he made some really great gains that year. But I think most importantly he didn't have to think he was stupid anymore.
I understand the PP that said some kids do much better on meds and don't do well when they are off them. I have seen that too. They really can help kids that genuinely need them. But I have also seen where they don't help and kids that are on them when they don't need to be. If your kid is falling asleep after they get their meds, than that isn't helping them learn at all. I have known teachers that push hard for students to be on meds, solely because they are behavior problems. . .they are much better behaved when the are stoned or passed out. I don't think poor classroom management is a justification to medicate kids. I also don't think it's ok to medicate kids if other things like emotional problems haven't been ruled out. Unfortunately, I have seen that quite a bit. Things like sexual abuse will mirror the symptoms of ADD.

JMHO.
But back to the OP. . .you need to be patient and really find out if your child is ADD/ADHD/LD. Whether you go through the school or have them tested by an outside expert, you need to find out what you are really dealing with before an appropriate plan of intervention can be determined. It's like spending thousands of dollars to treat your child for ulcers, only to find out they are lactose intolerant. It might make you feel better that you are doing something, but in the end you wasted a lot of money and have done nothing to help your child. Really think about that! Do you want to help your child, or just make yourself feel better? You have gotten lots of good advice here, from all sides of the spectrum, people that have worked with literally hundreds of kids over the course of their careers and parents that have gone through this on an individual level. They
all have given important things to be considered. And I think in the end, have said pretty much the same thing. You need to have your child tested by experts, find out what the problem is and then decide what is the best course of action.