YES!
YES!
YES!
But I think the game needs better balancing before tournaments.. so you have time to get it more organised.

The replay idea isn't terrably good because theres no rules for what settings, what maps, so on..
It would be nice if you had "flavors" to the tournaments.
Big maps only.
Small maps only.
Of course as you said singles, teams.
Vasari/Advent/Tec/Random only(these shouldn't happen often).
But until then just both teams agreeing on the map is fine.
Supreme commander had this.
I hope Demigod does!
I'd love to see this be something you do with Impulse on games that support it (IE sins and demigod.)
And I think it'd be good for Stardocks image to be serious with it's competitive gaming. (It is for supreme commanders)
ALSO someone mentioned that this would be good to find the elusive balance issues.. Well not nessisarily. People could look at the replay and what they think made a team win and what they think is overpowered and be terrably wrong. No nerfing light frigs because I killed someone by spamming them. That doesn't make light frigs overpowered, they obviously made some big mistake that made me able to win doing that, or moreso I took advantage of the situation and decided that would be best to end that person quickly and not take risks.