AFAIK if you're married you're married and immigration status has nothing to do with it.
On the other hand, immigration officials can decide the marriage isn't grounds to stay in the US.
It's best to not try to take the easy way out and to assume you're married until you've gotten the divorce.
If you're tempted to try to pretend it never happened you're giving him a lot of power to show up where and when you least expect it to make your life miserable.
Do what it takes to resolve things legally and following the rules.
we were both illigle imigrants.
Let me guess, each one thought the other was legal?