Just because the drive can never reach c doesn't mean it isn't still accelerating at the same rate.

A drive that accelerates at 10ms^-2 will accelerate at that rate until its power supply is depleted, and its kinetic energy will continue to increase in proportion to how much it has accelerated.

At high speeds you have to calculate kinetic energy differently to account for relativity, but it still works out to be the same value that you would get if there was no speed limit and you accelerated for the same amount of drive-relative time.

Going back to the 1g drive from before, if you accelerated for 10 years, your velocity would be around 10 times the speed of light ignoring relativity. However, relativity is a thing, so your speed would actually be in the realm of .99 c. In both cases, 10 years of time have passed for the drive, and it has accelerated constantly for those 10 years.

However to an outside observer in the relativity case, the drives mass, dimensions, and passage through time will all be massively distorted. It would appear pancaked in the direction of travel, its mass would have increased massively, and much more than 10 years would have passed

But the total relative acceleration done and the kinetic energy are unchanged.