Were talking about a starship's impulse engines, not some contemporary chemical fuel rocket. If you've got engines with the power to push a 190,000 metric ton ship to high percentages of light than those engines can easily push you out of orbit and out of the system. What's even more amazing is how powerful those engines are given their comparatively small size in relation to the rest of the ship.
However those impulse engines are dependent on how much power is available to do the pushing and where they happen to be.
We've seen in "Tomorrow is Yesterday" that if they are low on power and in a planet's atmosphere it takes a long time to just climb out of the atmosphere (or even build up power to start climbing).
We've also seen in times of aggressive acceleration like in "The Doomsday Machine", "Elaan of Troyius", "The Immunity Syndrome" and arguably, "WNMHGB" that impulse power can be used up very quickly.
But in times where they don't push the impulse engines hard, like in "The Paradise Syndrome", impulse power isn't a problem.
Pushing in a hurry a nearly million ton ship to high relativistic speeds or even low FTL speeds (depending on your interpretation) with impulse engines to Delta Vega could easily use up so much power to not be able to power back out of orbit.
Hypothetically, if they accelerated more leisurely to Delta Vega it might not be a problem to leave orbit, but by the time they arrive Mitchell would've been unstoppable.