no your time jump drive is not part of the ship, it's a P11 cloaked ring that sits around the ship, when we jump to new galaxies we drop it in the middle of nowhere so if anything happens to the ship we still have the time jump drive to fall back on. It is linked to the main ship and Capt has made it clear that he and no one he has access to can relink it to a new ship so if we lose the Wandering Star this might as well be lost as well but we still are careful since it can be damaged in firefights etc.
It's info you all should be housing in the bottle anytime you leave the ship or are in danger of being boarded or captured as well. Its clear based on some of the updated systems on the ship he had access to a highly advanced race at some point that did a bunch of things to the ship but he could never repair or replace things like the White Hole Generator
(White Holes are theories that cant even be proven in TL 9 societies and not only do you have one but you got something that is using a TRAPPED one to give the ship unlimited power (Which is what is needed for the OTHER crazy tech system that is your time jump drive which does not exist in any TL 9 society either (they have the choice of either stopping inside the ship and leaving outside flowing normal or outside the ship with inside flowing normally. NONE have the ability to do BOTH at the same time, their science tells them it's impossible(like White Holes) but here we are using one...
Scanners just come up with an error when they scan any of these systems. (other systems that are from the same level are the internal Time guns that freeze anyone not keyed who is the crew for like 12 hours) The Doctor inferred he knew something about what had done the upgrades but Capt quickly changed subject 😉