Coach, the NES one does do save states. There is an option in the menu you need to turn on (press SELECT at the ROM selection screen), then I believe it's something like Up + Start to load the state, Down + Start to save it.
http://http://krikzz.com/forum/index.php?topic=2554.0
The SNES version does not.
Also, it should be noted that they all offer battery saves (SRAM). When you save in a game (that supports it), the save is written to the SRAM, just like a cartridge. When you decide to switch to a different game, the SRAM is written to a file specific to that game, then the new game is loaded into memory, along with the new game's save file. I have actually pulled the saved SRAM file of a specific game and loaded it in an emulator to play. Then you can save in the emulator, put the save on the Everdrive, and begin playing where you left off. It's a neat little feature, though it does take a little hex editing sometimes because the 2 save files may be a different size (usually just padding the end of the file with FF).
They seem to have gotten rid of the original Everdrive MD v3. Now they just have X3,5,7. X3 and X5 doesn't appear to save states (my apologies), but the X7 does.
http://krikzz.com/forum/index.php?topic=5775.0
Ugh hardest game ever. It took me like 20 years to finally beat the 3rd rat race in Level 10, then get stuck on Level 11 where the giant lollypop looking thing chases you.