I'd imagine yes, you'd still owe them.
Years ago when I was having to watch every dollar I miscalculated once and incurred a pile of NSF fees at the bank.
Back then the rules were different, and they would clear checks and debit charges in 'high to low' order which would maximize the fees that were incurred. It was especially painful because I was out of work and every dollar was important. Making matters even worse was that several of the debit card charges were for under $5, but the fee they incurred was $37 - each. It would be another week before I would have any money to deposit, and by the time the 'dust settled' I was nearly $500 negative over a small error in my checkbook.
It was painful and caused a severe hardship, but I paid the fees. I would keep that checking account for a few more years before finding one with more favorable terms (although I will add that was the last time I had an NSF problem). Now the laws are different, and things are quite a bit more favorable to the consumer, but in any case it taught me a lesson... when it really matters, I'm very-much on top of my account balances now.
All that being said, I'm the last person to pass judgement on someone. I will simply state that in my case even though it was painful at the time I paid my fees, and I've never had to be concerned with Chex being an issue when opening a new account. I would recommend to the OP if there's anyway possible to clear up the old debt with the banks I would do so; things will be much simpler going forward. While the 'baddies' will eventually drop off Chex and other banks will likely let you in, you'll still have the SOL to consider for your particular state (dropping off Chex doesn't make the debt disappear). Also, don't forget EWS... many banks report to them as well as Chex.
Good luck whatever you decide. 