Besides the fortune needed to refit a battleship even in mild disrepair, running costs would be fearsome. These ships are meant to be supported by the resources of battlefleets, not solo operators. A sole battleship won't pay for it's own running costs. It'll eat a lot of income coming in from elsewhere. Perhaps best represented by less profit factor from endeavours or more misfortunes?
And there the possibility the Imperial Navy will resort to less open and less honourable methods of acquiring a battleship. A ruthless admiral likely has a lot of personal pull and more than a few allies to call on to cause "accidents" and trouble for a stubborn rogue trader dynasty.
If your players pull it off, fair play to them but obtaining and keeping a battleship should not be a pushover.
While I confess that, yes, it could, would, and SHOULD cost a fortune, I can imagine a few players willing to say it's worth paying the PF. If the ship was yours, and being rebuilt in the background, by your support NPCs, with you performing the big missions to earn PF, and then spend fractions of that toward the refurbishment, along with some of the more important RP moments, interacting with the big people you need to talk to to get some of the parts/work, it wouldn't even slow down the game much, and the pay out, a mighty warship that could scare even the Orks of the Blood Axe Clan's Deathburna. Every once in a while, they might just say "forget the PF, we have enough, for right now (slap for blasphemy), and just want one hell of a bragging chip.
I've never completely understood the stuff of "needing a support fleet". Nothing in the book says, "one reason few rich Rogue Traders often look past the Grand Cruiser Hulls is the need to have an escort fleet of support ships, carrying food, water, resources, and stuff." To me, a Battleship is still just a ship, a big ship, practically a mobile starbase, but still a ship, and one with plenty of room to store stuff. Certainly, with such a massive crew, the need to pull into port might be more common, limiting its time abroad, but tons of in-story battleships head out alone, and no one expected anything bad to happen. It often feels like a bit more of another excuse to keep the biggest ships with the NPCs, so that the Battlefleet can still have something bigger than "these silly space privateers." Besides, if I ever incorporated a salvageable battleship in a game, and it wouldn't be every game, much more rare, it would be near the end of the levels (7 or 8), and by that point, the party could easily have a ridiculous Profit Factor, and have already looted/purchased several "smaller" vessels, thus enabling the support fleet, if the party chose to plan smart. Certain threads here seem to say that enemy ships are often captured all the time, giving many Rogue Traders their own little fleets. Many of them act like their own Battlefleet, so I could see it, even if they might not make friends, that way. The number of other people who say their parties attempted it shows that it could have been done, so...
Now, the military being devious a-holes, and trying to do bad stuff, that I can see, and like. It makes going to the legit ports a risk, and that can make keeping a battleship less attractive. I rather work on the plan of there are no good people in 40k, so the military could easily say "sneak in a saboteur, and to hell with that writ we signed." It could open up a fair number of fun RP options, and possibly help the party see a need to go Hostile Acquisitions route, once the legit channels are shown to have sharks, too.
Despite how this reads, I don't want this to be easy. I want the party to have to work for it (even though my own knowledge would be hard-pressed to cover in-game what they would need to do (but that's what other people's posts, here and elsewhere, are for), and spend money in the tons, while fending off another interested RT, maybe some Orks, or whatever, and having to wait a good amount of time (not a quick process, rebuilding a battleship), but I'd like for it to be doable. Say, for instance, my party reached Lvl 7, and had done much of the stuff in the Expanse; while there will always be an infinite number of other things they could do. At this point, they sit down and say, "hey, let's leave this place, and go somewhere where the pickings are better. We're heading out to the Reach, to "assist in the Angeivan Crusade". There are numerous worlds there, where no person of our persuasion has been in ages, and the threats are much bigger, to reflect that the profits are, too." If they went there, the threats would be different, and much bigger. Tau Fleets, Tyranid Hive Splinter Fleets, some Orks and Eldar, the forces of Chaos with fleets, they all have more ships, bigger ships, and bigger guns, and this is where a truly massive ship could help you. The Crusade has bogged down for ages, and even just one Rogue Trader, with a big ship, and a decent fleet, not bound by their supply chains or command structure, could go a long way toward freeing up the Crusade forces to get moving again. Then, they could spend 1 1/2 to 2 levels tooling around in the Reach, make a ton of money, see how bad stuff there might be (it's made for Space Marines to be challenged), and head back to the Expanse, or retire. This could also open them up to wanting to play Deathwatch, once they can't level up in RT anymore.
As for upkeep of the battleship, I don't completely know how the game uses upkeep, but I'm sure that would be spendy, too. Luckily, the one thing most Rogue Traders are never in short supply of is money. Frequentish trips to worlds, for shore-leave, crew rotation/refreshing, and supply restocking should make even a battleship an ownable asset.
As a last little bit, I feel that if you did, say, find the Light of Terra, and you never did get the ship up and running enough to allow L-C Rothe to make his mad, misguided warp jump, say you killed him out of fear, if you told the Navy where their precious hulk was, they wouldn't do anything to go get it. They don't have the time. or resources, doing all of their military stuff, and they wouldn't want to pay to rebuild it, either; much less liquid assets than a Rogue Trader dynasty. That leaves it open to pirates, who might turn it into a space station, a place to store their loot, and launch their smaller ships from (sort of an island command center for the fleet) or, heaven help us, Orks. I can only imagine if a band of Orks found it. They'd have enough guys to swarm through it, kill all of the Tribesmen, eventually, and Orky tech the ship back into a semblance of functionality, at a much cheaper cost, and then the Imperium has to deal with an Ork fleet led by the Worldstompa. Better it be that Imperial assets retrieve it, especially at their own cost, and it stay with the Imperium. If the Trader goes heretic, at least his usual stops will be places where the military also has eyes, and they might be able to do something.