Not as far as I know. There is already both a serial port and a parallel port better suited for this kind of task. But it would be quite a neat hack, I agree 
I tried one day a long time ago, but it didn't work as well as on the TI-99/4A, though that required a pre-amp.
Yep, I think 16k (?) on the cartridge port can be mapped as ROM/RAM so you can access it at as such. There's also DMA, where the cartridge can grab the bus and move data at 1 byte per cycle. That's the only way to support that kind of transfer rate, and it's used by REU cartridges to transfer blocks of data from and to mapped memory.
With all address and data lines available at the cartridge port, it's possible to map the entire memory space to the port, but there are some requirements. Off the top of my head, I cannot remember all the restrictions, but I do recall some issues with the on-board address decoding done by the PLA, the data and direction port of the 6510 ($00 and $01,) and what-not.
The REU can DMA directly into and out of C64/128 memory, though I'm not as familiar with the C128 banking as I probably should have become. The REU has three commands: FETCH, SAVE(?), and SWAP. I haven't touched my REU code in so damned long (you guys really kill me when you dredge this stuff up, makes me want to dive right back into it,) but ISTR you put the REU bank, C64 bank, possibly the number of bytes to transfer, and then the command into registers mapped into I/O space at $DE00 or $DF00.
Fun stuff. REALLY fun stuff.