Chickens and guinea fowls will cross breed, but the young are sterile.
Question - do the females lay eggs?
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I can't say for certain as there doesn't seem to be enough research surrounding them but I do believe they would lay eggs.
Eggs from a "fertile" hen are all considered sterile until fertalised by a rooster. A hens egg is produced similarly to a human female with the expectation that she will reproduce regardless of whether or not she can or cannot successfully procreate. In other terms, in a continuous egg producing cycle until old age.
An exception to this case would be if the guin-hen hybrid had not been born with the reproductive organs required to create an egg.
It's notoriously difficult to breed hens/females of almost any hybrid, particularly in birds. In this experiment with a particular pairing:
Out of the 701 hybrid eggs produced only 1 hatched.
Which would explain why this particular subject is not thoroughly researched.
I did also stumble across this page. However, it does not seem to provide much information other than they have successfully bred hybrid hens. Unfortunately I can't find any information on whether or not those hybrid hens are active layers and the website has not been updated in a while although there's no harm in emailing them to enquire.
Finally I located this webpage which suggests that hybrid hens will lay start to lay around their 20th week and continue through the winter but cutting short at around 2-3 years. This page provides information for Chickens and guinea fowl seperately but does not specify its meaning of "hybrid" and whether or not that includes guin-hens.
I'll update this post if I find anything else that would suggest that a guin-hen can/not lay eggs.
I do not know anything about chicken. But a little about biology.
It all depends on why the cross breeds are sterile. In most cases the cross breed has reproduction organs but the cells could not match properly on a very basic level. In this case the body do not allow further steps for reproduction (like "pregnancy").
But if chicken in general could lay eggs without ever met a rooster the possibility is high that cross breeds could it too. I know they could play eggs without little chicken in it, but do they have to meet the rooster in before?