How well would training on an elliptical help with actually running?

Elliptical is a good low-impact exercise for recovery days, but as stated above, it is no replacement for actual running.

In my humble opinion, as long as you are doing cardio and pushing yourself, then that helps. I HATE FRIGGIN RUNNING, however, I do it because it keeps me somewhat thin and is good for the heart. And I simply refuse to be a fatty. I've had times where I've done nothing but used a treadmill for a couple of months a couple of times per week and improved my run time on the APFT. Every person's body is different and my upper body strength is what gets me the most points on the APFT, so I don't focus so much on my cardio training for the points and still achieve well over a 250 easily, and I'm fine with that. Doing interval training on a treadmill for a couple of miles is sometimes all I need to improve my run time. I mainly run outside on beautiful sunny days, only. I say don't over think it, just run, brother. Then run some more, either inside or outside.

I think they can be used as an effective rehab tool if you're coming back from injury or simply trying to give your legs a break from the impact of running, but I wouldn't use it as a replacement for running.