It's possible. You will need a lot of pins so a 2560 would be a good uC for the job.
A NES or SNES cartridge has:
- 1 or more ROM chips for the game data, sprites, music, etc.
- a boot ROM to authenticate the game to the system and pass the boot sequence
- 0 or more RAM chips for storing game save data - will be paired with a coin cell battery
- 0 or more logic buffer and/or inverter chips
- 0 or more RAM chips for system memory expansion/buffering
- 0 or more GPUs - So far as I know this was allowed for in the design but never implemented due to cost, but I'd love to be proven wrong on this point so I can buy and understand it better
Essentially a cartridge is typically a glorified read only parallel access ROM. Emulation of this with an Arduino is quite possible given the massive speed of 16MHz compared to the NES. To do this you must first understand the pin out of the cartridge, which I just happen to have: NES_Famicom_Pinouts.pdf (27.3 KB)
You will also need a copy of the boot rom. Which I have somewhere amongst my 2.2PB of data. Soooooo, you may have to search for it yourself or buy a couple cartridges and rip it.
But the big concern is Why?
Were I interested in the concept I'd much prefer to make an Arduino run a cartridge rather than emulate it.
Just my 2 cents.