I'd rather argue that it would be a question of pushing the ship from the relativistic speed she already possessed, to her virtual-standstill meeting with Delta Vega. The effort would then detract from the journey home, unless it resulted in the ship regaining her near-infinite sources of power; not making the effort would allow the ship to continue towards civilization, as opposed to being "stranded".
As for dialogue cues, the ship is first said to be heading home on impulse power, but then Mitchell warns Kelso not to "activate" the starboard impulse packs. This sort of suggests coasting after an initial boost...
That's a very good point. At the time before diverting to Delta Vega the Enterprise could have already committed (accelerated to a cruising speed) to heading back to the nearest Earth base and that could've used up almost half her impulse power. They had no reason to expect to do a diversion so any side trip to a planet other than their original destination (requiring full deceleration) could leave them without power to blast back out of orbit.