Look, I don't want to start a whole thing here, but here it is: Logistics is important to military operations, and any good military leader will factor that into their planning for the coming campaign. Failure to do so will usually guarantee a failure in the campaign to follow.
In short; if you can't supply your army, they're not going to last.
As regards the situation here:
The UEF has by virtue of the situation a very short supply chain. Except for the stations under GTVA control, every resupply point for the UEF fleet is only a jump away, and their production base is in the immediate vicinity. The GTVA has almost the opposite situation, their supplies in Sol are dependent almost entirely on the logistics ships, which have finite supplies, and their production is on the other side of Delta Serpentis, several jumps away at best.
(Side Note: The GTA almost certainly does not have a heavy resupply capacity near the Sol-Delta Serp node; this is strategically unwise, should UEF forces make a successful push through the node. Likely there are at least some supply points there, but most of it is either spread out in Delta Serpentis, or more likely in Beta Aquila, Vega, and Antares.)
As said, the GTVA supply situation is almost totally reliant upon the Anemoi-class ships, one of which the UEF has already captured. (Do we have a number for how many of these are available?) Indigenous supplies of weapons and equipment will usually be useless for GTA forces. (Though the foodstuffs will probably be kept if only for the novelty value. Soldiers sending pictures of themselves eating actual real-live Earth food back to the family in Laramis.) Basic electronics parts may be of use, too, however in all, this will represent a minimum of supply potential for the GTA--they will much prefer to be using their own equipment from their own resupply ships--all of which is already spec'd for use and doesn't need to be half-reverse-engineered before installation.
At the same time, the GTA is an invading force, which historically is much more costly than defense. Unless they have several aces up their sleeves, which they would've been foolish to have held back this long, they needed to prepare ahead of time for a potentially long and violent campaign. The 14th's successful entrance into Sol (which somebody fouled up for them in AoA) would've probably countered this dilemma, if they could've pulled it off.
All this ties back to the points made previously in this thread and forum--the difference in design philosophies between the GTA Terrans and the UEF Terrans. To use a modern times metaphor; the GTVA is a deepwater navy, while the UEF is a littoral (coastal) navy. Both are good at what they are designed to do, and have a little overlap in terms of purpose. When it comes to one challenging the other on its home turf there will be advantages for each. The metaphor breaks down a little, because in the end, they're all spaceships that can operate apparently anywhere in deep space, but bear with me here. The essential premise seems to be the GTVA has adequate performance and long range/duration. The UEF has very high performance potential, but short legs.
In keeping with the original premise of this thread, let's assume the GTVA wins the war. What do they do with the remnant UEF navy?
Well, for the most part, most of it will probably stay in Sol under new management. Almost immediately, some examples of each ship class will be taken to Fleet R&D for testing and analysis. See what works, what doesn't. Find out how compatible each ship is with existing GTVA systems, and what the costs of retrofitting would be. I suspect a few of the fighter/bomber designs could be reworked to incorporate Balors or Maxim cannons, just as an example. The cruisers and frigates would probably be retained until the end of their operational lifetime as patrol ships and defense escorts, if only because they're already built and in place. As for the Solaris destroyers, I suspect they would be kept around by the GTVA as carrier ships, not unlike the Hecate-destroyers. Without back-checking, I can think of no reason they couldn't be loaded with GTVA fighter designs and repair equipment. Retrofitting them with GTVA weapons (not necessarily beams, either) could prove problematic, though.
I didn't want to make a whole long post here, but it just sort of mutated as my thoughts came up. I haven't fully thought all out, but I'm sure somewhere on here this discussion has been had at least once already.