It 'might work', I think. Particularly if you haven't changed the location of the XAMPP folder and didn't make a lot of changes that re now hard to recall.
You should 'diff' (compare for differences) the Apache .conf files, to catch any changes in there. They are found in \xampp\apache\conf. For the ones in 'extras', you can simply check the file modified date to see if they were altered, if so 'diff' the altered ones.
A good tool for this is WinMerge (its free). You can use the same tool for your php.ini and/if needed my.ini.http://winmerge.org/
You probably could coax mysqldump.exe into backing up your database by using the command prompt. Changing directory to \xampp\mysql\bin on the old drive and then using mysql.exe or mysqldump.exe to get a backup.
I'd say try it, you have little to lose.