interfacing SRAM with classic Gameboy

If you take apart a classic gameboy cartridge it basically just has an addressing chip and a ROM chip on it. Would it be feasible to take out the ROM and instead connect the addressing chip and the rest of the addressing pins directly to a set of SRAM chips?
For example you'd have a circuit powered by the arduino that would write into the SRAM chips connected to the gameboy through the cartridge and when it's done you could turn on the gameboy and it would read from the SRAM banks. This would mean two circuits have only the SRAM chips (and the relay) in common. A relay would shut down the arduino circuit the moment the gameboy is turned on so there would not be double the voltage going through the whole circuit but also the SRAM would never be without power and loose it's data.

Is this at all feasible? Am I overlooking something? I reckon that a capacitor should smooth the flow during the switch from one power source to the other. The other concern I have is wiring the SRAM to the cartridge. Would it still be responsive enough for the gameboy's processor? From what I've calculated the SRAM should be fast enough but I'm worried about the latency the wiring will add.

The point where this breaks down is that the arduino does not have enough memory to hold enough code.
There is no need to shut the power down you don't double the voltage.
Data select chips will work for switching between the two systems, as long as the two work on the same voltage.

This sounds like a problem that dual ported RAM was created to solve. Have you considered this? What is the operating voltage of the gameboy anyway?

James 4CS: Cool! I looked all over for someone who'd already done this but the only thing I could find was somebody who built a rom dumper.

Grumpy_mike: I'm using 2 256k sram chips I've repurposed from other devices. I'm feeding the arduino the rom data over the serial line. This part already works.

JoeN: I''ll look into that. I think it was 5 volts.