There is definitely a difference in speed between debug and release modes. In debug mode, everything is slower because there's a ton of extra code being executed to allow the program to know what line it is running on and handle breakpoints and unhandled exceptions.
Having said that, it usually doesn't cause people's games to run slow. Usually games are runnning so fast that the computer is sitting around waiting between frames.
So, yeah, if you use GameTime instead of just assuming that the game is running at a particular frame rate, you shouldn't notice any real problems if you're seeing that dramatic of a change in performance.
OH WAIT…. Are you saying it is FASTER when you're debugging? That's very odd. When you say "published" version, are you talking about something that is running on the Xbox 360, or just running it on the PC, from within Visual C# Express without debugging? I know the Xbox 360 handles some things differently—like garbage collection. I made a game once that created tens of thousands of objects (and by that I mean just simple classes, not game objects being drawing on the screen) and it worked fine on the PC, but on the Xbox 360, it was incredibly slow, because of the difference between the two. Do you think you could provide some more information about what you mean by "running through your published application"?