I love fruit beers but I think you would get the same or better beer adding plain old peaches and bourbon to a secondary. Whereas you could use the jarred peaches in something lke a pie, dumplings, homemade ice cream, more bourbon, etc where you would get more out of something that sounds pretty unique.
If the jarred peaches are as easy and cheap to get as plain old peaches then it wouldn't hurt anything to give it a try. The usual fruit recommendation is to start around 1lb per gallon added to the secondary and adjust to taste.
I am not sure how to get the most out of the syrup without it just adding sweetness. I wonder how much character it would retain if it was used as the priming agent at bottling/kegging.