Played a game as TEC Loyalists today. Could have won a lot faster, but decided to take it slower to play with the various new toys. Corsev was... Interesting...
Boarding Party should be able to damage/heal ships larger than frigates, just not take over them. Also, looking at the buff chain for it, I could be mistaken, but it looks like it doesn't even need to be the one to kill the frigate for you to get it, though I don't recall ever actually getting anything. This ability seems like in it's current iteration that it would be effective early on, but I got it as my fourth capital (after an Akkan, Sova, and Dunov) at which point it was pretty much worthless.
Demolitions Team is an interesting ability, though I wasn't ever really able to find a good use for it. Once again, this seems like it would work best when your full attention can devoted to one ship, aka the early game or on very small maps. Heck, I was playing Gaian Crescent which only has 16 planets and it was still too much.
Salvage Operation: I like the idea of this ability. It allows the Corsev to regen a fairly large fraction of the health of it's fallen allies, making it very powerful indeed. This ability already makes the Corsev more or less immortal in larger battles, so it's not an issue. I find it odd that it can't regen health from fallen capitals or structures though. Not a big deal as it's already quite powerful IMO. This ability definitely turns the Corsev into a tank. A very flat, centipede shaped tank.
Elite Crews: This ability is largely worthless, not to mention the fact that despite having a Kol nearby, it kept casting the stupid buff on my Sova which didn't need it as it was busy kiting. Aside from that, it buffs a single target capitalship. You know when that's useful? Early game.
That ship, though it has powerful abilities, requires micro unlike anything else in the game for many of it's abilities to be remotely useful. Because the Akkan is the better choice in the long run for a starting capital, we can presume that most will not open with this ship, meaning that the highest priority ability for upgrades will likely be Salvage Operations. A point in DT is probably going to happen in case the ship needs an emergency heal and some points will probably go into BP, but only because it deals a DoT, not it's ability to capture. All I'd suggest for it would be a range increase to 6500 and allow it to heal allied ships.
Elite crews on the other hand.. Increased damage per bank targets is really the only thing I can think of here...