Some additional facts to the 1541:
The C128 drives are supporting additional modes. The main differences between the 1570/1571 and the 1541 are
- 1541: single sided, 35 (40) tracks, GCR recording (not compatible with DOS or CP/M formatted disks). Capacity: 664 blocks (254 bytes each). Very slow serial IEC bus (serial version of the IEEE488 bus). There were many software and hardware floppy speeders available which made the system much better.
- 1571: double sided drive, fully compatible to the 1541 (and also very slow). In this mode also single sided. Additional modes for 128 mode with enhanced speed and double side support and a third mode for CP/M support (different recording system).
So yes, it works definitely to use the 1541 with a C128 - but it will have only the performance of a C64 floppy disk even in C128 mode.
I've never owened a C128/1571, but a 1541 in combination with the original C64 and a hardware floppy speeder. So I'm quite familiar with the 1541, but all I know about the 1571 is what I've read over the years in the 2nd half of the 80s.