The on-access scanner scans every file before you, ehm, access it, and it doesn't matter if it's on a hard drive, network drive, flash drive or anything else.
If you're asking if avast is making a full scan of the whole drive though, then the answer is No, and I don't think that would be a good idea anyway (depending on the size of the drive and the number/size of files stored, it may take a lot of time).
Cheers
Vlk