Well, in theory, this has no other answer to be yes. Although I haven't tried that myself, I have my answer backed up LOGIC.
Say you're trying to get the Flying medal. Now, there is only one pure Flying type, and that is Tornadus / Tornadus-Therian. So you would probably need an entire team of Tornadus to get the Flying medal. And GameFreak doesn't expect that, as you will probably get one (the Therian one from the Dream Radar). Therefore, it must account for dual types.
Yes it does work, I've tried it several times.
I beat the E4 with 4 Tyranitars and got ground/dark
aswell as bug/steel with 3 Genesects
Yes you will.