Yes, if she seems lethargic it's probably best to see the vet.
It could simply be that the male isn't feeding her enough (I know mine would almost rather starve herself than leave her eggs for more than a few minutes) - that could be the case since they're inexperienced. However, since egg binding is a possibility, a vet check is needed.
With my GCC, since she has no mate to feed her, I give her handfeeding formula twice a day when she's on eggs and a snack of a few walnut pieces once a day. When she's laying eggs, she simply refuses to eat her usual food - it seems like it's not calorie dense enough to be worth her time to eat it. Sometimes she will come out to be fed before I have her formula ready and she will completely ignore the dish of chop on her stand and cry with hunger... and if I'm not quick enough with making her formula, she will give up and fly back to her eggs without eating anything at all (of course I take her out and feed her when the formula is ready).
I guess my point is that it takes a lot of energy to produce eggs and if he's not feeding her enough, so she has to leave the nestbox to eat, then she may need some extra rich foods to help support the egg laying. Handfeeding formula is a good choice as it can also help cover dietary deficiencies from laying, but just to get some extra calories in her, you could try some nuts or unsalted peanut butter mixed with her regular food.