Answer:
It depends on your parakeet.
If the parakeet is a female over about 4 months old, they are capable of laying eggs
If it does not have a mate, it usually will not lay any eggs, however its possible. Obviously these eggs will be infertile and will not hatch
If she does have a mate, they will lay eggs as long as they have access to a nest box and breeding stimulus (such as extended daylight)
It is healthy for a parakeet to lay up to 2 clutches of eggs a year. A clutch is usually 4 eggs. Any more than this and the birds health is endangered. Egg-laying uses up the calcium in the female bird (hen), so you will need to provide her with cuttlebone.
Dont attempt breeding your birds unless you have thorougly researched it first.
good luck