Or will I have created a split brain scenario?
You've technically created a split-brain when you did this: >At this point I would have to force the Window cluster service online with force quorum [...]
Now coming back, when the links come back online will SQL1 and 2 go offline as soon as they see SQL3 is active?
Long and the short of it is that SQL1 and SQL2 will have a different copy of the data than SQL3. You need to decide which one of those is the "correct" copy. Since SQL3 was forced for quorum the cluster services on 1 and 2 is going to resync with it and it's copy of the cluster, which means everything on 1 and 2 is going to go down. The databases don't match but they were forced failover so they won't attempt to automatically reconnect. You're going to have fun restoring databases on the node(s) that you choose don't have a correct copy of the "truth" and most like forcing failover again.
Basically, I wouldn't do this. There is a reason it's called a disaster recovery option and not a "Test your BCDR" option. There are better ways of testing.