Precisely, and painfully obvious to those familiar with the respective fictional phenomena. The scenario is a trap for the deathstar, but posing the scenario is a trap for casual fans of scifi. (Still quite worth the exercise.)
I still remember straining my eyes rolling them so violently upon reading someone's question about Q and the douwd. My instantaneous impulse was to point out the douwd's inability to truly bring back his wife, quickly followed by about a dozen other obvious reasons Q was the "stronger" of the two. I can't discount the possibility that the question was intended an act of trolling.
Now if a star destroyer were to be substituted for the deathstar in your thought experiment, and was piloted by a savvy enough captain, it may have affected escape in much the same way as the enterprise.