[EDIT]

Based on further research (read: exactly one DDG query) It appears the Action Replay is actually significantly more complex than I had guessed and functions differently enough from the Game Genie that they quite often simply cannot operate in tandem like this and can cause serious issues.

Read on if you'd like a cool story that has little to do with reality, or would like to imagine how chaining game genies might work if that was feasible :3

[/EDIT]

Based on my (admittedly not incredible) knowledge of how those devices both work, they intercept reads for specific memory addresses from the CPU and insert their own values. As long as they both weren't set up with codes to modify the same address very little would happen, it would behave as you might expect.

If the two both had codes that modified the same address the Game Genie would "win" here since it is physically closer to CPU in the chain. It would see the address matching one of its codes and spit back its value, neither the cartridge nor the Action Replay would see the memory read occur.