One possible problem is that the battery covers are designed to hold the external SD chip down into its slot. Without a cover in place, there would be some risk that the chip, if you were using one, could slide up and lose contact.
Regarding using the stock battery door instead of the extended battery door, well, it does snap on, yes, and it sure isn't going to damage the SCREEN on a Droid3, eh ?
That said, I've been running mine that way for a week or two, and I have noticed maybe a problem...when typing longer stuff on the slide-out keyboard sometimes I am now noticing "ghost" keypresses causingg doubles (see?) or stuck-down keys ! Sometimes, even, the backspace key will come on and eat up a bunch of my recently typed text. I also get an odd screen come up displaying foreign alternatives to a key I just hit, which I then have to clear to continue.
I had not considered these might be related to battery size pressure, but may be. The reason I used the smaller battery cover with the extended battery is because the black nobby rubber 2-part case Verizon sold me with the Extended battery, saying it would fit together fine, does not. The larger part, the back cover, will NOT stay on over the extended battery door, it pops off over the upper right corner of the phone's back. Fits fine over the regular battery door, regardless of what battery is in.
It looks and sounds like the Qmadix case is the same thing.
Glenn