Can you do it? Sure.
As you said, you are basically making extract, then doing a partial boil. I would probably do 2 five gallon batches back to back instead, with full-volume, no-sparge BIAB.
FYI, I have a 15 gallon pot, and even that does not really have the capacity to mash a full-volume, no-sparge, BIAB, 10 gallon batch. It's big enough for the boil though, so after mashing I can drain off a few gallons into a bucket, and sparge with a few gallons. My next BIAB system will use a 20 or 25 gallon kettle, lol.