I'd argue signings or acquisitions like Hossa and Kessel, or even guys like Niskanen or Oshie helped put teams over the top before they won the cup. So no their base isn't built through UFAs, but it is pretty common that teams need to be aggressive when it comes to the final couple of pieces at times.
I don't want something stupid like Hayes at 7M for five years, but it is time to be aggressive IMO.
I think for comparisons sake we should avoid the use of cap circumventing deal like Hossa's. Also Oshie was traded for and not a UFA if I remember correctly, although they did resign him.
When we look at those teams though what we notice is that they already had their cores in place that were good enough to win Cups without them but with their addition as depth guys they did help.
An example of a good UFA signing would be something like Ian Cole. Good role player but not really the reason you would win or lose.
I have stated in a few places that the Avs are now actually in a position where UFAs could make sense but I wouldn't go far enough to say its time to be aggressive. We are just starting a 6-9 year cup contention window, so while its justifiable to look to get better in the now, I also don't feel there is a large rush. Also the Avs have some pretty big unknowns on the team in Barries future, this years 1st rounders, Bowers, Timmins and Kaut that will all have a large impact on the Avs and their future needs, so it may be a bit early to fully commit to certain types of players right now.
There is certainly a good argument for making some win now moves, however if the Avs simply do nothing other than D&D they will still be in a very good spot. The only circumstance in which they lose is should they lock in big money to the wrong player.