No, the cookie wouldn't have to be rewritten, it's already done by UBB.classic, if memory serves.
Uhm, I never tried this add-on on 6.3.1.x,
as I primarily made it for 6.3.0.x.
UBB.classic went through lots of changes (especially all the Control Panel templates) in 6.3.1.
I still have to "port" this to the newer UBB.classic.
Somewhere at UBBDesign.com is a simple script to read the user's cookie and to retrieve the last date/time of visit.
I just don't have any URL, but my bet is on the archives.