Yeah they're definitely going to share that the battery's there - they could help out with connecting it to the screen in the lounge, but it also looks like Zari is going to work on having all the ship's power up in around a weekish so either way the screen should be up by that point (as long as the circle members who need food/water don't run out by that time)

edited to add: it occurred to me that since the comments I linked to above mention Zari working from the thing Hank and Connor discovered, they'd probably know she was working on it, and Hank would totally direct Mettaton that way if Mettaton seemed interested in helping Zari get the electricity up a little more quickly