I can't say I've ever heard of this but, that's pretty incredible. I'm sure the baby will be just fine from the anesthesia. As for a regular pregnancy I'm really not sure but I am sure your dr will monitor you and baby closely for most if not all your pregnancy... best wishes
At that stage I don't think the anesthesia would effect the baby. But pregnancies after tubals can be serious from the sounds of it you got pregnant before and although not the idea situation I think everything should be fine and develop properly