Can the NIOS II f be used as a dropin replacement for NIOS II e?

Yes the cache is the main difference between the cores that can cause problems with the software. If you still want to use the speed bump provided by the cache, you need to change the way you communicate with your components. You can use uncached addresses (I think the function to do that is called alt_remap_uncached() IIRC), or use the cache control functions to flush the cache after writing and invalidate it before reading.