Short answer: Sometimes. :)
In some cases, a bank is willing to accept offers on REO listings. Banks may list with an online host and schedule an auction 30 days in the future but allow "pre-auction bids" prior to the sale. Not all banks do this. But if a bank allows the bids, you can offer your highest/best and if they accept it, the schedule online auction will be taken down/cancelled. Sometimes I hear from customers who say they were watching and watching a listing then suddenly it disappears....and it's because they accepted an offer so the sale is closed/removed.
In many cases, the online bid will start at a low 'grab attention' price because that works well in the larger, more populated states. In smaller states like Missouri, this model is annoying because it isn't the "reserve price" as the the opening prices. So investors note that they may bid many times without hitting the reserve and not win.....although I have heard of some buyers who said the bank accepted the lower 'offer' when it didn't pass reserve status....so there are opportunities out there!