Hold on, if there was no U.S.S. Velocity, then wouldn't that make this the Enterprise class (at least referred to in the parallel universe)? Because with very little exception, there is always a class ship. My reasoning is that the name Velocity must have come from somewhere. It would make sense if the Velocity didn't exist in this universe, but it had to have existed in the other universe.
I agree with you in Starfleet not literally sending the Enterprise back to her universe, but I think they would have research done in how to open a rift to the other universe, and send try sending a probe. After all, the crew of the Enterprise must be worried about their family and friends, and would want to know if they are okay. And I doubt that the other universe would have collapsed in on itself so quickly. Perhaps the portal would have started acting like a black hole after the universe it was connected to collapsed. The worst case scenario I see is that the collapse of the universe results in some sort of shockwave, which would then proceed to obliterate anything in the E-F's universe that it managed to reach (similar to maybe a huge gamma ray burst, but omnidirectional), before the portal acting like a black hole. I would think that there would still be enough time for the governments in that universe to attempt to do something.
Not only that, but once the beings who created the portal in the first place realize that the universe that it is connected to is not only collapsing, but also threatens their universe as well, wouldn't they not only try to close the portal, but also accept help from the Federation in that universe?
On the other hand, it makes sense that Starfleet might try experimenting with the singularity drive by building a small batch of Velocity class vessels. Due to the fact that they are dealing with something from an alternate reality, it might be classified for the moment.
But because The Seeker was built here, that must mean that she must have a history in this universe. Since you haven't yet come up with a history for her, I'll just speculate, if you don't mind:
The original Seeker, NCC-1801 (like I said before, change it back, so that it doesn't conflict with the U.S.S. Clemenceau) was a Constitution refit class, Tikopai sub-class. This makes perfect sense, given that the U.S.S. Tikopai has a registry of NCC-1800, making The Seeker the second Tikopai class vessel built.
After a long, successful career, like most Constitution class vessels, this Seeker is decommissioned. At the request of the crew, who have gained enough respect in Starfleet's circles, not only is most of the crew assigned together to their next assignment, but their next assignment is given the same name, and given a registry of NCC-1801-A, similar to the Enterprise.
I have two suggestions for what the NCC-1801-A can be. Either the NCC-1801 can be decommissioned towards the very end of the 23rd Century or the very beginning of the next century, and be replaced by a Renaissance-class cruiser, which is sort of a smaller version of the Ambassador class, and preceded the Ambassador class by a few years; or the NCC-1801-A can be an Ambassador class, built between 2300 and 2310.
The NCC-1801-A could be a victim of the short Romulan-Federation conflict that resulted in the Treaty of Algeron, similar to the speculated fate of the Enterprise-B, and be replaced by a Korolev class Heavy Cruiser, since the Korolev's registry suggests she was commissioned in the early 2320's.
The NCC-1801-B has a long career, surviving the Dominion War, and other various conflicts of the later 24th Century, but is destroyed during the ongoing Klingon-Federation War in the 2400's.
Soon afterward, it is chosen to name the first Velocity class heavy cruiser under construction in this universe the fourth vessel to carry the name The Seeker, with a registry of NCC-1801-C.
My apologies if I seem too presumptuous in trying to assume The Seeker's history, but the way I figure it, ships with a letter need to have a history for them; why else would she have a letter registry, and well, you haven't written a history for her yet, so I figured I would try helping.
