Well, if the speed of light happens to be, say, 1 inch/million years, turning off the engine could take a while, since they won't be able to exceed the speed of light while reaching for the off switch.
But seriously, technologies based on "controversial theories" (generally nice scientist speak for "bullshit") have very little chance of ever appearing.
And while I agree with Mufasa that many great strides have been made by people who weren't constrained by the current thinking about various stuff, there is also the fact that most of the low hanging fruits made available by scientific progress have already been plucked. Most of the progress in the last 100 years has been derived from our understanding of quantum mechanics; very little "breakthroughs" have occurred since.
In fact, other than miniaturization, there is very little new technology in the past 30-40 years. Nanotech and biotech show much promise, but that's not being done by guys in their garage, nor is most of it applicable to FTL travel.