Yep.
Most if not all 'free' games are really just adware. Like said, the developer has to get paid somehow. Paid games are ad free or at the very least, ad reduced. (I've paid for my angry birds app but still get ads for their other products and games)
You may also want to vet the games. Some developers are more easy to work with than others. Read the reviews and look at the ratings. There are some 'games' out there that are nothing but ads and very little game. This will usually be reflected in the ratings. Download cruddy games, get cruddy ads.
If you haven't already you may also want to restrict in app purchases since most games anymore are 'free' but want you to pay to play via in app purchases. If your children are playing games unattended they could rack up quite a bill without even realizing it, so locking out in app purchases is a way to protect against that.