I've not seen anyone book a "consolidator fare" or anything of the sort using the Chase travel portal. As far as I know, they're only showing published revenue fare classes like you'd find on delta.com. Regardless of what combination of miles and UR points you use, the full cost of the fare will be "purchased" from Delta by Chase, and it will show as a revenue flight with the proper MQMs and MQDs for the fare class bought.

A couple of years ago, when Chase couldn't distinguish BE fares from non-BE, I called in and asked to book a specific fare class - they were able to price it and buy it over the phone. These days I don't think that's necessary, but if you want to be sure, you can always call and ask.