If the chickens are shut in the run all day, you need to be sure they have shade from the sun, shelter from rain, food, water, nestboxes if they are laying--all the things they could usually go inside to get.
Yes they have all of that as it’s connected to a shed with food water bedding etc .
Is that the same shed you have pigeons in?
If you let the chickens out and then close the door to keep the pigeons in, that also keeps the chickens out.
Or do you mean you have several sheds? If so, I'm not sure why you want to put pigeons in with chickens at all. It's usually easier to provide the right conditions for different animals if you house them separately.