As I recall, Voyager was chosen to hunt down Maquis because it had the tactical power and maneuverability to work well in the badlands. So long as that mission remained, I suspect that Voyager would return to DS9 from time to time.
The Enterprise was also assigned at some point to the same region of space, and visited DS9 as well as other starbases which were presumably in the area. The Enterprise was reassigned sectors a number of times, so it stands to reason that Voyager might have been reassigned to other sectors if the need arose.
Voyager would have likely participated in the Dominion War if it had stayed in the Delta Quadrant.
As for the change in characters, the Maquis crew members would have likely end up destroyed by the Dominion (unless you consider that the Val Jean could be sucked up by the caretaker, but not Voyager.. that might be interesting)
Janeway might have turned out to be a competant captain if she were closer to Starfleet. I think her character originally had potential to go somewhere but ultimately failed miserably. If she had the guidance of other captains and admirals, she could have turned out a lot better.
Kim's progress would have been interesting to see. I always thought he was the most interesting character on the show, but he never got much to do, or room to grow. A lot of potential for him there.
Paris would still be in New Zealand, and I'm okay with that. I liked him as a friend to Harry, and as the pilot, but he never really sold the "antique americana" thing fully, it always felt like something they tacked onto him. His medic aspect is pretty much worthless. He didn't add much to the show.
The Doctor would have likely remained deactivated most of the time, and therefore would never learn to sing Opera, which would be a vast improvement.
And of course, Neelix and Kes would be stuck in the Delta Quadrant, though if the maquis was sucked in by the caretaker, they could annoy Chakotay for 7 years, and I wouldn't be bothered by that at all.
Seven would have remained a drone, which I could either take and leave. Seven wasn't horrible, but I didn't think she was awesome either. Icheb on the other hand, was pretty cool. Too bad for him.
The rest of the crew (the Maquis people) were pretty bland and uninteresting, and I think that's the basis of why Voyager fell so flat as compared to the other trek series (though, I suppose Enterprise had some pretty bland characters too).
Yes they did -boldly go- in the same sense as TNG, but the circumstances were vastly different.
When people think Star Trek, they think of "exploring the unknown" as an essential element of Trek, and I agree with that, but it is very possible to overdo it, and the show creators really packed it on with Enterprise, which is ultimate what killed the franchise.
The best episodes of Trek are not about "boldly going" anywhere.
TOS: City on the Edge of Forever - the most critically acclaimed TOS episode: Kirk returns to 1920's Earth. This isn't "New worlds and civilizations" this is old world.
TNG: Best of Both Worlds - a fan favorite: The crew fights the Borg in Federation space, even returning to Earth in the process. No new worlds here, and even the borg we had seen before.
TNG: Yesterday's Enterprise - a fan favorite: The reprecussions of the Enterprise-C travelling forward in time in Federation space. The crew fights the klingons. No new worlds, no new civilizations.
DS9: The Visitor - a universally accliamed episode: Jake Sisko spends an alternate lifetime in an attempt to rescue his father.. a lot of it spent on DS9 or Earth or the Defiant. No new worlds, no new civilizations.
DS9: In the Pale Moonlight - a fan favorite episode: The moral consequences of espionage in Starfleet. The Romulans are involved. No new worlds, no new civilizations here either.
Obviously, exploration and new worlds are an integral part of Star Trek, the dominion, breen, and cardassians are all excellent examples of new civilizations that were discovered in later Trek, but these are all just a means to tell a story about the human condition. Star Trek works best when it explores humanity, and doesn't work when you're changing course to scan down a class 2 nebula.
I think a major reason why I dislike Voyager is because the writers spent a lot of time on the "how" and "what" of the plotlines. (how many times did Borg Nanoprobes solve the episode's problem?) They didn't spend enough time in the "who".. but when they did, Voyager really did work well. In particular VOY: Imperfection is an example of a Voyager episode done right.