Absolutely.
I've just been introduced to the game. I come from a long history of competitive gaming. When I do something, I do it to be the best in the world at it. I don't really just casually do something.
Right now, Dominion (isotropic) is something that I'll play when I only have 15 minutes of free time (kids do that to your life), or when we're at the cottage and I want to play a board game with non-gamers that has more strategy than monopoly.
If Dominion were supported competitively, I would probably get into it bigtime. It would probably be my game of choice.
I'd love to see weekly dominion tournaments at my local card store (which btw, would probably love to support it), and yearly state/provincial championships, which seed players into national championships, which seed players into the world championship tournament at Gencon (suggestion).
I'm actually very surprised that there is little to no competitive support for the game. I've found that making "idols" (i.e. stars, world champions) is amazing for the growth of a game. For example, look at the poster-child of MtG. I played that game since beta. My friend and I used to collect black lotuses, because our local group thought they were junk (we did too btw). My friends mother threw his collection into the trash, because she hated him playing it. He had over 100 black lotuses in that box she dumped (ya, I know, holy smokes).
Before MtG had a competitive scene, it was a game that you may see kids playing in the caffeteria, or stairwell at the school. It was played on kitchen tables, but you never really heard about the game. Once they started supporting it competitively, you had pros, you had names to look up to, you had articles to read, you had entire websites open up, devoted to strategy for the game. Card stores started holding local tournaments, you got to meet more people in your community that played - that you would have never met otherwise. This led to more games being played, more product being purchased, etc.
My local card store also does a Saturday intro-day, where they will demo card games all day long. It's normally stuff like Pokemon, MtG, World of Warcraft TCG. I've asked him why he doesn't demo dominion, and his response was that he generates more sales from the other games, because once he gets people playing the game, they come to the supported tournaments and buy more product. There is very little in it for him to hold a Saturday all-day Dominion demo event.
Once you make stars of the game for peiople to look up to, and tournaments for people to go compete at, you really start to take the game to the next level. Sure MtG and Dominion are different (in terms of collectable card game vs boxed game), but that doesn't stop chess from being supported competitively.
I (personally) think that any game that isn't supported competitively can only grow so far, then it hits a glass ceiling. Even games like scrabble are supported with world championships.
I go to Gencon every year, and having world championships for your game really makes it stand out. Just the signage and volume/buzz that is generated serves to infect nearby spectators, and people go and buy the game. They then play it at their local card stores in the supported tournaments, and before you know it, your game is growing exponentially.