If the Atari 2600 could do it, pretty much anything can.

IIRC, the 2600 had one service that would do it over a dialup modem, and another that got the data from your local cable TV company.

There is a YouTube video out there of what I believe is a Russian dude copying a Dendy or Famicom cartridge through sound, though. The system is powered up with the copier cart. The copier cart copies its code to the system's 2K of RAM, and runs from there. You then remove the copier cart and insert the game you want to copy. This makes the screen garbled as you are removing the graphics data from reach of the PPU, but the code continues to run as the CPU is not reset. The copier cart will then iterate through each byte of the cart and emit FSK tones through the system's audio out which you can record and then convert to an .nes file with a utility. I suppose it has to know the mapper involved and such.

But there's no way for the NES to shove that modulation through a separate audio out (and definitely no real audio input).

Now the Famicom/NES does have a few GPIO-like lines through the expansion connector, so bit-banging a UART I guess would be possible (if appropriate converters for the voltage are present), but it couldn't be very fast as the CPU has to service the PPU every frame with OAM DMA writes if sprites are enabled.

The Commodore 64 RS-232 built-in capability was driven entirely with software and it didn't go faster than 2400 baud.