I think I understand the question, and the answer is YES. If Time Machine has backed up the contents of drive A to drive B, you can retrieve them from drive B even when drive A is not available.
However, you can't use the fancy Time Machine interface to do it, since that only works when the original folder is open in the Finder (unless there's something I'm missing). Instead, navigate directly into the Time Machine backup folders. The file structure of Time Machine's backup is pretty straightforward.
Inside the "Backups.backupdb" folder on your backup volume, you'll have one folder for your computer. Inside that folder is a bunch of folders with backups from different times. Despite the fact that only newly-changed files are copied with each update, every one of these folders contains a complete image of the disk at that time, using "hard links", which essentially make one file appear in multiple places. Open one of those folders (or the "Latest" link) and then just pick out the files you want.
I just tested this myself to be absolutely sure, and yes, it works.
P.S. I completely misunderstood the question at first, too, since the original post doesn't mention Time Machine except in the subject line.