There isn't much information about the safety features of Carpathia. Rostron answered a couple of questions about them at the US Inquiry:
Senator SMITH.
The fact that, under these regulations, you are obliged to carry 20 lifeboats and the Titanic was only obliged to carry 20, with her additional tonnage, indicates either that these regulations were prescribed long ago - [Rostron had earlier testified that Carpathia carried 20 lifeboats.]
Mr. ROSTRON. (interposing)
No, sir; it has nothing to do with that. What it has to do with is the ship itself. The ships are built nowadays to be practically unsinkable, and each ship is supposed to be a lifeboat in itself. The boats are merely supposed to be put on as a standby. The ships are supposed to be built, and the naval architects say they are, unsinkable under certain conditions. What the exact conditions are, I do not know, as to whether it is with alternate compartments full, or what it may be. That is why in our ship we carry more lifeboats, for the simple reason that we are built differently from the Titanic; differently constructed.
Note how Rostron describes how newly built ships are "practically unsinkable", but he does not know exactly why; he makes a speculation about watertight compartments. This implies that Carpathia did not have watertight bulkheads. There's no other information to the effect that I could find.
Carpathia carried 20 lifeboats, the same number as Titanic. Someone else will have to scrutinize the available photos and drawings of Carpathia in order to determine the breakdown of emergency boats, 'regular' lifeboats, collapsible boats, etc.; I have seen photos with as many as six lifeboats per side in view, suggesting that there were 12 boats in the davits and 8 alongside. If we assume all 20 boats had a 65-person capacity, Carpathia would have had 1,300 lifeboat spaces, which is more than Titanic -- but recall Rostron's assertion that Carpathia's lack of watertight compartments warranted more lifeboat spaces. Carpathia would have had emergency cutters, as Titanic did, but the decrease in seats due to two 40-passenger boats is not large.
The best figure I can find for passengers aboard Carpathia is 740; there were about 300 crew. That means, in theory, that there were probably enough lifeboat spaces for everyone aboard. (Note that this will mean that the inquiry into the loss of the Carpathia will not come to the conclusion that ships should have enough spaces for all aboard.)
So, in this scenario, Carpathia will be catastrophically damaged. It will be instantly obvious to all passengers and crew that the ship was doomed to sink. This would mean the rescue operation would begin sooner, with respect to time after the collision, than Titanic. The ship will sink very quickly and may well capsize.
The worst-case scenario, I think, is that Carpathia launches proportionally as many lifeboats as the Lusitania was able to launch (6 out of 48 = 12.5% of boats = 3 boats, rounded up). Next most likely, Carpathia launches six boats, the same number as Lusitania, but in a different proportion. That is 145 spaces in three boats or 390 spaces in six, which corresponds to 14.5% and 39%, respectively, of the total passengers and crew. (On Titanic, about 32% of those aboard survived.) Of course, the boats will not, by any means, be full.
That's just speculation, though -- the notion that Carpathia would have sunk about as quickly as the Lusitania -- on a subject where a mathematical answer can be derived. I can't quite figure out what numbers are needed given Carpathia's tonnage and buoyancy versus the influx of water from 12 square feet of damage, but many others on the forum will be able to do so.
