I was born in the US and my parents registered my birth at the Thai consulate, which got me a Thai passport, but I was never registered at any Tabian Baan. Moved to Thailand when I was 27, and had to partake in the draft (literally stuck a hand in a giant jar to yip bai dam bai daeng). I'm not sure what triggered it, Tabian Baan registration, national ID card, social security... so much paper work. Anyways, it took me 3 trips to get my registered on my family's Tabian Baan, they were just so difficult, no one at the office had ever seen a consular birth certificate and wouldn't sign off on it. Was very frustrating. I can only imagine how much harder it would be to get a consular birth certificate decades after the fact.
This was awhile ago. Maybe their systems are integrated and linked now, but probably not. What I would explore is if you could just get your consular birth certificate and Thai passport only. If you are not on any Tabian Baan then probably will avoid the draft. You are required to enter/exit Thailand on your Thai passport, but I'm sure your child won't be the first to use his US passport. If your kid ends up returning before they are 30, can deal w the draft then, it's not that hard to manage.