I'm just about to solo and I have about 200 hours prior experience with an instrument rating. So far, it has helped some but not an immense amount. Having the IFR rating definitely gave me a leg up in the instruments academics and in the sims, but it also highlighted me to the instructors and they expect me to be good at that stuff. In the presolo contact stuff it hasn't helped too much, honestly. Maybe that I have a little bit of a clue what's going on and a small amount of air sense (not much SA yet though), but the flying is WAY different, the radio calls are totally different, and the expectations are just as high for everyone.
I can't speak to how it will contribute to my overall success or failure during UPT, but my previous flying experience has helped some. It definitely helped at IFS because that was essentially civilian flying with a different traffic pattern. IFS, however, is pass/fail so being the best with 6900 hours or showing up with 0 hours doesn't matter. As long as you work hard and aren't UNSAFE you'll do fine. That's basically what they've looked for at UPT so far, too. "Is this dude unsafe? Will he kill himself or someone else if he's flying by himself in the pattern or to/from the MOA." If you're safe, you'll succeed, if you're unsafe, you won't.
Back to your question -- it depends. It definitely helped on some of the academics tests, but it has hurt in some other areas from using previous techniques that don't work. For example, I had a bad habit of a high flare on landing. I flared early and settled to the runway just like I did in a C-152 and Piper Warrior. Problem is with the T-6 that's not how to land. So, I had some negative transfer and got hosed on my first few flights for ending up in a sinking flare situation. After a few debriefs and clarifications I realized (through some IP insistence and demonstrations while airborne) that I was doing that from my previous flying. I didn't know it, didn't realize it, and now I don't land like that anymore. So, weird things you didn't think would be an issue become issues, I guess is my point.
Also it's important to recognize that you will be instructed as if you had 0 hours when you show up. If that chaps your ass and you get an attitude about the "remedial" instruction then you are doomed to failure. Having a good attitude and being humble about your previous flying experience (and all other things) as well as helping out the guys who are struggling in the flight is the most important thing, I think, about previous flying experience. but for you, with 0 experience, don't worry about it. The program is designed for 0 hour dudes to succeed. There are lots of guys, some on this board, who showed up with 0 hours and got what their first choice out of UPT. You just gotta work hard and study up. If you know the procedures the IPs will teach you techniques. Don't waste time you could be learning techniques having them teach you the procedures you should've already learned.
HUGE CAVEAT: Remember, I'm just a STUD, in the baby class, and I haven't soloed let alone earned my wings, so take what I said with a big grain of salt. There are many more experienced people here who will have better perspective than I do. I'm just telling you my experience in UPT thus far. Whether you still want to track t-38s and MAYBE get a fighter after T6s depends on whether you a) like pulling g's and strapping into an ejection seat b) like wearing a helmet, mask, harness, and g-suit every day to fly, c) don't suck at formation, and d) want to be a fighter pilot after meeting some and learning what the days are like behind the glamor of it all. There's a lot more to it than I ever thought there would be, and it's way different than I expected. There is definite appeal to both sides. Don't pigeon hole yourself to flying fighters because you saw Operation Red Flag or Top Gun and you think want to fly a pointy-nosed jet around.
Hope that helps.
I know your question is relating to have no experience, but I kinda answered it from the other direction. Sorry for being a little verbose. PM me if you want more info (not that there's much more to say...)