That is a possibility IF your COA (label with Product Key on it) is for XP.  If you purchased it from Dell with the downgrade from Vista to XP, then it will likely have a Vista COA on it.  If that is the case, you can downgrade to XPx64 Pro, but you will need to call Microsoft activation to activate it as per the downgrade rights.
Hello,  The small company that I work for have two Dell Precision™ T3500 Workstation's and they want to upgrade the RAM in them, however it has a 32 bit version on Windows (Vista) but downgraded to XP and so have a 4GB limit.I have read on some other posts I can request new 64 bit install discs provided that the machines are within warranty. Is this correct?  Thanks  RustyBadger.
Windows - Upgrade to 64 bit Disc