Are you talking about the Motorola extended battery ... codename BH6X?
I've been running mine with the stock battery cover for about 3 months now, without any issues.
To better address your question, though, I ran my HTC HD2 with an extended battery, no battery cover, and the Otterbox Defender case, for over a year with no problems.
This is definitely a viable option, if you're worried about stress to the screen with the stock battery cover. I doubt you'll miss the cover. The case provides more than ample protection and eliminating the battery cover will probably aid in cooling the battery, if nothing else.