Well, honestly, a lot depends on how he handles it. If he just signs child support checks and that's it, probably it won't have a lot of impact on your relationship. If he want to get involved, then things could get ugly, emotionally speaking, and fast.
Realistically speaking you're under zero obligation here. To be honest, if you really think you can't take the drama, it's time to walk away. I would wait and see what he does and how he copes before making that call, but as cold as this may sound, if you can't deal, it's better to end it now.