Can I create an unbranded version of my property site for the MLS that doesn't show agent contact information or company logos?

Yes, just append /mls to the end of your URL or custom domain name like this ...

"Unbranded" MLS link using a custom domain name.
http://www.615hampton.com/mls

"Unbranded" MLS link using default CribFlyer URL.
https://cribflyer.com/615-hampton/mls