I had kicked that idea around as well at one time. It was a neat idea that would have put a fun spin on the Enterprise's history. Unforturnately Delta Vega isn't far enough. I'm sure they travelled as quickly as possible and I'm sure there were some relatavistic effects while doing so. But even at .99x C where they'd age hardly at all they'd only be a couple of days out of synch with "real time". (It might be that they took a few weeks getting to DV, but then you're close to time as experienced by the rest of the universe.) Then there's the fact that going by the actor's ages they're only a year older between WNMHGB and Corbomite Manuver (going by production rather than aired order). So it's not unreasonable to assume a gap between WNMHGB and the regular series.I wonder if the Enterprise might have turned off whatever relativity-limiters they had on the impulse engines (or simply accelerated to the impulse speed where relativity starts affecting them) in order to reach Delta Vega faster to them than the rest of the universe... it would certainly explain where the first two years of the five year mission went, and why the Enterprise underwent a subsequent refit immediately after and uniform fashion suddenly changed.
Ah, I hadn't realized that the dilation effects were so low even at .99c...
BTW, my take on the series refit is that the damage to the Enterprise by the barrier was fairly extensive. Also exploring out of the galaxy was not part of the "Five Year Mission" as such. So to solve both problems the ship was docked and upgraded. Not really backed up on screen, but it's a fun notion.
I like this. It fits pretty well with my own assumptions, too.
