Can the SSI overpayment hit my checking account for not paying back the overpayments without telling me first?

You can't pick and choose which creditors are included in your bankruptcy. The SSDI debt will be included in the bankruptcy. And, yes, unlike private creditors, the government can levy your bank account without proving the debt to a judge. That's because - once upon a time, in a land right here, there was a just and fair government that didn't lie to get money. Now we have Obama and the government lies all the time and nobody trusts it but it can still take your money without proving it.

You should not assume that you can LEAVE OUT any debt when you file bankruptcy. Bankruptcy law requires you to include EVERY CREDITOR so unless you want to commit a crime, do not decide that you will not file against some creditors.