Is it possible to back up the files that CCleaner has selected to be cleaned prior to finalizing the cleaning?
No. Well, yes, I suppose you could do it, but not with CC.
Nor really would you want to, the default ccleaning is only mostly temp files and Most Recently Used lists
if you aren't using winapp2.ini and haven't added any INCLUDEs, then CC (out of the box) does not remove personal data, only system crap.