Now THAT is an epic awesome post: yes, yes and more yes. Generated content is the way to go. The way design is now, it can afford to be a lot more than just a mad gab. They can have variables for tactics and call the names from a database, one that could be updated and also contain variables for past dealings.
It would take a lot of writing, as was also pointed out... instead of 100 sets of dialogue for 100 static missions, you'd have to have thousands of lines of dialogue for 1 mission, that happened to have 100 variations.
As for consequences and feeling like you're part of the universe, I'm not sure if I said this before, but 'mission chains' might be the way to go. Basically, mission chains mean that every mission carries with it the history of events that led to that mission. It'd be pretty dry, I'd think, and read like battle feed:
"On Planet Archid in the Venga system, Capt. Velor defeated Pirate B'el Tasar. B'el Tasar fled to the Klingon-Cardassian Neutral Zone and attack the Kibosushi Maru. B'el Tasar defeated Commander Sam Duckets and escaped with 400 latinum worth of goods from the Kibosushi Maru. B'el Tasar is now attempting to sell these stolen goods on Aenor, see Mission Briefing for more info."
While this may seem dry, if you know Velor or Duckets and talk to them about their mission wins/losses, then this becomes exciting... you're part of a continuous universe. What that means is, that every mission, whether lost or won has to be able to generate a mission. This means that a GM event will spin out a great deal of new missions of fallout, or, with a little fudging, GMs can spin existing mission chains together to 'spawn' their GM event. Some missions might be high stakes, and so it could spin out several missions that other players will end up dealing with.
This is the other place where writing has to come in... writers need to be creating new planets and NPCs as old ones get destroyed. They can, by and large, continuously recycle assets like dialogue, clothes, faces, pallettes, minor races, as long as its mixed and matched. The database has to be consistently added to with new options to keep the game fresh for hardcore gamers.
That's how I'd make players feel included... mission chains string everyone together into the same universe. You can trace your mission back to a major event. Of course, some mission chains will just get started by GMs, but they'd still have some kind of origin, perhaps 5 minute mini-GM events would generate these things. Just someone playing as Quark at the bar lets out word of something serious... boom. New mission chain.