Of course, you could be lucky. It could work out of the box. But it is true that "shelf-life" is actually worse for a cap than a working life.
Cap manufacturers usually specify a "shelf life" in their datasheets (f.i. 1000 hrs., do the calculation, and this is about 41 DAYS). This shelf life indication is the moment that the manufacturer guarantees that the product will meet the specifications. So you could say the caps are "over" specced a bit when they leave the factory, but already after 41 days it's down to it's published specs.
Imagine 25 years of shelf life.
Still, as mentioned, it could work just fine.
F.I. The Sanyo monitor on my Nintendo cab has one of the nicest pictures I have in my collection and I have replaced only one cap because it had the famous fold-over problem. Maybe if I do a full cap-kit it will even look better, and at least you will extend it's lifetime and prevent problems in the future. For the little money a cap-kit costs, I think it's worth the effort.
I would at least test it before you do the cap-kit because if there _is_ a problem you don't know if it's because you made a mistake on the cap-kitting or that it was just bad from the start.
Here's a handy map for your cap-kit job:
