Bummer. 
I didn't realize the protocol droid parts weren't compatible with the astromechs too. Weren't all Hasbro's BAD parts compatible regardless of how stupid it looked? Go figure that Disney didn't do it.
To a degree, I believe so. I can experiment more tonight if folks want. But for example, I can put protocol droid arms & legs in the holes on an Astromech torso, but a protocol droid head doesn't fit into the socket of an astromech where the dome goes and an astromech dome would be loose/easily fall out of you tried to put one onto a protocol droid torso.
For simplicity, I'm referring to any droid that has a torso, two arms, two legs and a head as a "protocol" droid.
The BAD BB units do consist of four parts, but three of those four parts are the weighted ball and the two halves of the outer "shell" of the droid. It's not like you can take half of the outer shell and use it with parts from another type of droid and cobble something together.
The BB-8 head/dome does have a socket on the top - I figured it was for one of those silly hats that Disney BADs come with can be inserted - I haven't tried one yet though.
One thing that is interesting about the BB-unit 4-pack is that while the bodies are all the same just with different paint ops - the heads/domes are all unique. So I can definitely see this as Disney's way of eventually transitioning to having build stations where you can build BB unit droids as well.