The rubber flooring would definitely die a short death, it would get wet and not dry out for days, its like a sponge, it will get mouldy and perish because of the moisture/sun.
The power rack would survive outside but i would reccomend some serious care. Get a can of spray on silicon (kinda like WD40) and coat all the welds and joints, and if you start noticing surface rust in any areas, scrub it off with a nylon scourer or fine steel wool and recoat the area with Silicone spray. If possible store your bars and weights inside. perhaps you could come up with some sort of on wheels solution to move your weights and bars inside and out easily, you dont want to leave the collars exposed to the elements.