In my experience most Lao passport holders just enter Thailand visa-free under the bi-lateral agreement. Although it only gives them 30 days, they can still do unlimited border runs. Paying for a tourist visa is not usually considered worth it, as it only gives an extra 30 days.
My 3 year old British son goes to pre-school here and we needed to show my, my wife's and his passport when enrolling in the school. He has an Extension as my dependent. To be honest, I'm fairly sure if he hadn't been here legally, it would not have been an issue, but I'm cautious about these things!
My only worry would be long term if you want the child to go to school in Thailand. Having overstay stamps in their passport might be a problem for some schools. If it's not a hassle it might be better to keep them legal.
has said, they don't care at the airport, and when you do your next report, 90 days after you return to Thailand it will still be shown that you did the one in August even it was late.