Shouldn't matter, no. I tested it with all four colours of teams, and on multiple maps before posting it just in case. That said, I'm on a Win7x64 machine... I didn't think that'd change the pointer path, though.
Tomorrow I'll ask my wife where she's hidden the power cord for the XP-based laptop I have and have steam download DD to it so I can test the trainer on that to see if I can duplicate the problem, and if so, I guess I'll find a solution to it!