It will stand, mostly because its a good idea to allow players who are geeked out about grey knights, but since I was the big pusher for the barge back when we were working on it, let me explain my mentality.
1. There is a new grey knights codex, not giving them something big and glittery would be extremely short sighted and a quick way to turn people away from the fleet.
I don't see what has that got to do with fluff but sure, for GK players, a nice, big ship could be given. But even a ship the size of a battlecruiser should be fine and not as huge as a battle barge.
2. Grey knights are the ones sent in to eradicate other space marine chapters who have been determined to be excommunicate. These chapters usually have fortress monistary's, two battle barges, planetside bases and fleets of strike cruisers and escorts. Not giving them something that can stand up to battleship level fire is just contrary to their purpose.
It's why they can call on the IN. They're the ones who are supposed to handle the topside while the GK and other ground pounders handle the groundside.
3. They are still a space marine chapter, and the only one fielded on Titan. The idea that they would not have a barge with Mars so close by baffles me. When you have the best equipment and tech priests at your fingertips, you never, ever say "no no, we want something smaller."
But who's going to man it? Servitors? If that's the case, its pointless. It'll just be shot out of space by other SM chapters. A cruiser sized ship already requires thousands of conscripts. What more a Battlebarge?
4. When dealing with large demonic threats, like demon worlds or demonship fleets, strike cruisers and escorts alone would be easily outmatched. Without access to battleship level defense or attack, they would not be able to do their job.
Lucky for us there's still no feasible daemonship fleet. Even then, the GK can still handle the lot of them if they are gathered together. That's how cheesy they are. And again, they do have access to battleship sized ships and large fleets. It's called the IN.
5. Its a damn pretty ship! I just wish we had the psy-cannon on the prow.
Yes, this is the only reason that would allow for the existence of one, esp if it followed the lines of the FW SC. Psycannon is too powerful I think depending on which iteration. I can imagine the Psycannon working something like an NC, doesn't scatter or does more damage (D6+2 for example) and does something nasty vs daemonships but that's about it.
Work alongside the navy? Not likely.
Most navy admirals would loathe the presence of grey knights ships. They tend to kill any normal humans they work with to prevent knowledge of what they fight from spreading.
Sure they would if the Inquisition tells them to.
other space marines? not likely, mostly for the same reason. The presence of the grey knights would suggest that the Inquisition does not think the chapter suitable for the task at hand, which is a pretty significant insult.
This is probably true until they face a daemon which they cannot fight. Won't be as much of an insult then.