What Star Trek needed back then, was a fresh new concept. The original plan for Enterprise (having most of season 1 set on Earth, with the ship launching at the end and us actually seeing this brave new world we humans we're trying to build) was a great concept.
Sadly, the studio's execs thought different. Braga and Berman got a lot of shit for Enterprise, but a lot of the things they did were forced on to them by the studios, because they wanted the more 'traditional' Trek, with technology people could recognize from earlier shows and connect with. Sadly, that gave the hardcore fans something that actually didn't like. Meaning that, the 'traditional' Trek appereantly didn't work that well anymore.
So, short answer... no. A series set straight after Voyager and basicly giving us more of the same would have died a quicker death than Firefly.