Yes Reptyle I do, from my experience it's not recommended to connect your game on an external USB hard drive, it will slow down your game because the speed of information going through your previous/original connection (SATA or IDE) is much faster than the USB external drive data transfer speed.
Everytime you start UT2K4, or even load a map while you're playing is going to make the system top ask and oad that information from an outside source and in youir case it's your new outside USB drive I guaranty you that that will make your game way slower and even unplayable.
My suggection to you is to move all pictures, videos, music, documents to the new USB hard drive and only install softwares, games and applications on the main drive (C drive), also do a SYSTEM CLEAN UP, that will help you get rid of all the dead and temporary files.
Bottom line it's not a good practice to install softwares outside your main or slave drive unless you really know what you're doing.
If you need more help on how you can Clean you System let me know I will write some steps for you, but make sure to move all big files THAT ARE NOT SOFTWARES to you new USB drive or record them on DVD's and CDs