re: No . . .
The ion drive was already an established scientific fact, with researchers the world over pounding away at it. Such imaginings as "warp core, impulse power, matter/antimatter, and trilithium crystals" point to -- nothing at all. And there are far better propulsion methods than a beam of light.
Do not study Star Trek engineering too closely, for you will become lost in non-science. That's one reason it's called "fiction". The idea of the author is to grasp a thread of real science -- or even minor speculation -- and pin it into something gloriously real. But this is done merely for the enjoyment of the reader, not to advance any form of hard research. New ideas may be gleaned from such, but none to be banked upon.
Dan