In my limited experience putting in cash offers on REO’s, cash seems to always speak louder with the banks. Meaning they will likely consider a lower cash offer with no contingencies over a higher regular financed offer with contingencies such as inspections.
I think if you put in a cash offer and put that in the contract with your offer the bank wouldn’t let you change it to conventional financing. From what I’ve seen most say they have the right to reject the deal up to the day of closing so they could just pull out of the deal if you try to change from cash to financing.
It has been my experience that banks are fine with offers using conventional financing as long as you’ve been pre-approved. Let’s face it, most “Cash” offers are either financed through a hard money lender or conventional lender. Most buyers don’t show up with cash
There is an old saying " Cash is King" and its especially true when you are buying from a bank. A cash offer means you can normally close quick and this is what a bank is looking for. The quicker the deal the more they like it.