Not quite.
Under 'normal' conditions a warp field is generated around each computer core.
Then you have Impulse power with its low level effects of space-time management.
Then you have a computer core itself. Until recently I have not paid attention to just how much power a Data Center can take. I mean just outside of the City of St. Louis a major building project is under way, when completed three (?) Nuclear reactors will provide 1.2x10^9 watts of power. This means that the computer cores of a Galaxy class Starship, which are supposed to be 100 feet tall, and sixty feet in diameter are major power users. Which further implies that better designed circuitry is in place. (Less power, required)
Such that a matter/antimatter reaction would be required to power just one computer core.
My thinking on this would require two reactors, with each able, for a short time able to both primary hull cores.
With the primary hull Impulse engines, plus the above...