Yes and no. Experience no. But skills wise yes. I worked all last year with nothing but UPT students and once you get through there you definitly have a solid foundation to build on. If you've got 5k hrs in a single engine or light twin you'll be just the same as someone who only has 1k when it comes to getting into that jet. Just different systems.
Once you meet the min requirements I feel you'd be good to go. I've never met a UPT graduate who didn't have what it takes. The training there is much more difficult. Like I said though that's once you have the time. Right now you aren't ready but by the time you get to 1k hrs you'll be a leg up on just about everyone. Just my opinion though.