Oh yes, they are definitely fertile.
I was going to do that at night but every 2 out of 3 people I ask say that if I move her and the eggs, she may lose her desire to finish sitting on them?????
This is my opinion and thinking. You will also understand why I come up with this conclusion..
Maybe the 2 out of 3 peeps are wrong. When a hen goes broody, she does so due to hormone influence. In order to make one get out of broodiness, there are tricks peeps do to have this come about. One practical way is to put hen into a wire cage with a wire bottom inside the coop. Keep her as a prisoner in cage, but do feed and provide water. No straw, or towel under hen. This chills her belly and broodiness ceases after a few days. Hen returns to laying eggs after a little while. That is the most common reason to stop broodiness. Peeps just want them eggs.. YOU EAT............... YOU MAKE EGGS.!!!!!!!!!!!. So if you prepare a nice nest inside coop ,, grab the whole clutch of eggs, and place into nest. Then place her into a comfortable nest on her WARM EGGS
WHO WOULD LEAVE..
I have hens go broody on me every so often.. Have no rooster, so no fertile eggs. They sit on other chickens eggs as well. I just steal those eggs everyday, and the hen doesn't even realize it is happening. It doesn't bother me that she is broody . Eventually they stop being broody on their own . My goal is not to get as many eggs as possible. (that is my goal, and others have different views) My chickens are PETS only... If they are not laying due to weather, daylight shortage, molting, or just plain not feeling like doing so, Its fine with me. They are PETS.
People that raise chickens in serious quantities do need to be concerned if the egg production is down.. I DO UNDERSTAND THEM ALSO.