Will color safe bleach help clean cat urine?

no. Nothing works on cat pee except replacing the item.

It won't do much for the scent of the urine. If the urine patch has dried, you will need an enzyme based cleaner. This is the only thing that has any chance of getting the scent out.
Bleach is also very dangerous to use to clean anything involving ammonia. When you mix chlorine bleach and ammonia you get a toxic gas.

I know that chlorine bleach is dangerous to use to clean cat urine. When the ammonia in the urine mixes with bleach, toxic fumes are released. Bleach also increases the ammonia odor, making it more likely the cat will resoil the area. I do not know what the ingredients are in Purex 2, but would not choose to use it to clean cat urine. An enzyme cleaner or CO2 cleaner would be more effective and is perfectly safe. I like a product called Fizzion, personally, but there are a variety of choices out there.