The fact here is, that an 1541/71/81/whatever Commodore disk drive, is a microcomputer on its own, so it can work independently of the computer. This allows the X1541 cable (which you can buy at
http://sta.c64.org, if you can't be arsed to make it yourself) to send data to the drive, which will then work by itself, like if it was working with a Commodore.
An Amiga drive is not intelligent, thus, it relies on the computer's controlle, and the serial port is no controller.
I hope I made myself clear, and that your question is answered
AFAIK, the Parallel thing in CCS64 allows you to use an emulated parallel conenction drive, not the real drive, but I can be wrong. There is a way to connect your 1541 drve to your C64 thru a parallel connection, allowing for faster speeds (like with teh Plus/4 drives), and I think this is what the emulator is referring to, but if someone knows otherwise, correct me. It'd be bloody brill if it could use the 1541.
Cheers,