Awap, we agree, train on your gear every time. For clarity, there are a broad number of air integrated inflators, and while it looks like scubapro air2s has had this good feature that enables you to push the deflate button and inflate from the mouth piece for a while, it's also good to know that not all air integrated inflators do. Also, it's worth noting that not all ScubaPro Air2s have a rectangular button.
The point is that gear changes from year to year and not all gear operates the same. So your main point is right on the money- train with the gear you have.
I have the fifteen year old Zeagle Octo +, which was OEM'd from APEKs. Like the newer Zeagle Octo Z, Aeris ION, and a bunch of other air integrated inflators, you cannot inflate by pushing the deflate button and breathing into the mouthpiece. This will deflate your BCD. Instead, you have to flip the air integrated inflator over, breathe into an inflator port BEHIND the deflator button while depressing the deflator button. Then all is well.
So... Good on you divers! Train with the gear you have!