Sealing plywood edge and faces (Shed Floor)
Do you need to seal the faces? Not really in the conditions you described. I have worked in a plywood plant and all the product used the same glue. The difference was the quality of veneer and if any holes were plugged , and later filled and sanded. The last step they did spray the edges and put the company logo on the side of the unit. 
Painting the surface will be plenty of protection, paint will seal from moisture and mud on shoes and actually provide some wear protection. Sealing the edges won’t hurt but really is not going to make much a difference in your conditions.