You will have a difficult time clearing the pool with the condition of your pump and filter. If the replacement is within the next two weeks, I think I'd get the circulatory system up and running so you can apply your chemicals correctly....circulation is virtually mandatory to clear algae out of the pool.

Now, after all that, It certainly doesn't hurt to put in some clorox to sort of hold the algae at bay....that'll make it somewhat easier to clear when you get your equipment running. You'll have mixed results doing so. I would concentrate on getting the mechanical portion correct ASAP then you can devote your full attention to clearing the water.