I encourage you to practice, watch videos.
Yes, red dots are and can be used eyes both open. Typically non magnified red dots are designed to do this. Your other open eye will super impose the red dot on the target. Aimpoints are designed this way. It is actually the idea of the red dot.
I use aimpoint the aimpoint pro for business and competition.

Cowitness is used for typically for LEO use so that you can always make sure your rifle has at least one set of functioning sights. You never have to worry if your duty weapon has been damaged after a period of time in the trunk or just getting beat around.

After you zero your red dot you will likely NEVER use your rear iron sight. But almost always when I open up my case for comp use I flip up the rear to make sure both are congruent then I put it down.

BUT Yes you can use the sight with front cover down both eyes open. It is absolutely designed for that. This is why Aimpoint have a clear rear cover. Its amazing to do.