Theoretically possible if you elide the requirement for negative energy density and negative mass, perhaps, and feasible if you allow for your ships to store literal tons of antimatter. We have no idea how to do any of that at the requisite scale, which is why all the popular articles about "warp drive" start with Star Trek references and never get any deeper from there. It's a blatantly aphysical black box.

This is, I feel, a massive problem in the context of a roleplaying game, because as soon as the PCs shoot through or melt the warp drive -- and in my experience this is inevitable -- we're back to making up magic for the sake of the story. Wormhole FTL at least has the advantage that a sufficiently perturbed wormhole can plausibly collapse into a singularity and thus be kept safely away from prying eyes, and a wormhole terminus is a superficially physical object that the PCs can chuck around.

And yes, I'm working on a system that's mostly concerned with encumbrance and skills. I'd have used Torchbearer's slot approach, but it feels wrong to limit the amount of mass/volume that can be moved in microgravity instead of it simply becoming continually harder to move and more expensive in terms of propellant as mass increases.