OK, I made a few tests. Please note that I have the package, whatever it is called, that puts up the "enter date" dialog on boot up removed. My phone boots up straight to desktop every time.

Test 1: Remove main battery for 5 minutes. Put it back, power up. System tme is preserved.
Test 2: Remove main battery for 2 hours. Put it back, power up. System time is reset.

So it looks like the bupbat keeps some charge but not for very long.