Our university actually DOES connect the flight and ground portion. To the University, they see "AVI-101" and "AVI-120" as classes. At the end of AVI-120, you get your PPL.

One of the things a few people did at our school, was enroll in AVI-380 (which is to get your multi-engine add on) a couple times using their GI bill. They got about 50 hours of multi time that way