Budgie hens can lay eggs regardless of the presents of a male, just like chickens. If there is no male in the cage the eggs will not be fertile.
Budgie hens cycle in and out of breeding condition, just like all animals. Mother Nature has made birds highly efficient. In the non breeding season the reproductive organs of birds shrink up to almost nothing. This makes the birds sleeker and have less weight to lug around. When birds go into breeding condition their reproductive organs once again swell and fill out for use. This can give the impression some birds are pudgy. During this time a hen's cere (the fleshy part of her nose above her beak) will turn brown and can get a crusty/flaky look to it.
Just because a hen is in breeding condition does not necessarily mean she will lay an egg. Nor does it mean she is unhappy if not working a nesting box. If you are not prepared for breeding and have read up at least a little bit on the subject this should not be attempted. There is a lot that can go wrong and birds should not be a new breeders learning curve in lue of learning even the basics. There are a lot of good books on the market for this subject. If your local pet shop does not carry them try looking for them here:
http://www.ABEbooks.com. I have ordered books as far away as England and Ireland and have NEVER had a problem. They have always arrived at the estimated times provided by each bookstore who listed the books they are selling.
If the hen does not appear to be in breeding condition, evidenced by the visual aid of her cere, she could have a tumor. There are lipoma - fat tumors which are soft and squishy. These can be handled by drastically reducing the fat intake of the diet. The main culprit for this is an all seed diet. Switching a seed junkie over to a healthy diet takes time and patients. No bird should be on a 100% seed diet. Seed should only make up about 30% of the birds diet, the rest made up of fresh fruits, veggies and bird pellets.
The other tumors are hard. There is nothing to help control these tumors.