It’s a cool idea, and admittedly would be a sort of loophole, but it might just mean that such a drive would require an arbitrarily high amount to work. Maybe Stephen Hawking was right and as soon as you build a machine capable of time travel, turning it on blows it up, because of QM effects. It does seem a little neat if how we intend to use the machine is the deciding factor in how it works.
Back in his collection All the Myriad Ways, Larry Niven wrote a brief essay called "The Theory and Practice of Time Travel" that explored ideas like these. One excerpt:
> GIVEN: That the universe of discourse permits both time travel and the changing of the past.
> THEN: A time machine will not be invented in that universe.
> For, if a time machine is invented in that universe, somebody will change the past of that universe. There is just too much future subsequent to the invention of a time machine: too many people with too many good motives for meddling with too many events occurring in too much of the past.
thus
> Niven's Law: If the universe of discourse permits the possibility of time travel and of changing the past, then no time machine will be invented in that universe.
