Even assuming that tech has evolved to a point where you can generate enough thrust, what fuel are you feeding these tremendous engines with ravenous no doubt consumption rates for 2,500 years?
Since you're bringing up scientific realism, the engines (apparently fusion) actually only need to fire up to get the planet up to speed rather than for the duration of the journey (Newton's laws and all that), once it's moving at say 1,200,000 mph (4.5 light years / 2500 years) it won't need to fire up again until they need to brake! As it takes roughly 354 days to accelerate to light speed at 1g (9.81m/s) the engines would only need to run for a few tens of years (obviously still needs to tick over to provide heat and energy so the folks on the 'wandering earth' don't freeze).
Lots of other scientific issues with the movie, but fuel consumption shouldn't be one of them! Well a bit of kudos to them at least they didn't do the worm hole thing