Using SHIFT + F4 will remove the background and leave on the sprites. Only as you feared, everything is replaced by black, which is a color used in many sprites, so someone would have to hack in that option. From checking FCEUltra's site, development is apparently still alive, albeit limited at the moment. You could try asking the coders there to include such an option.
At the moment, I usually use FCEUXD, a port of FCEUltra with a lot of extra debugging features included, among them the ability to see all the sprites and background tiles in memory. They won't be the right colors of course, but you'll at least see where the border of a sprites are, in addition to being able to fully see tiles that are sometimes only partially visible on screen.
Hope that helps a little
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Current projects: Ristar-The Shooting Star (Gen), Sonic The Hedgehog (Gen), Sonic CD (Sega CD), Mega Man Zero (GBA), Battletoads (NES), Bucky O'Hare (NES)