I'd say it's possible but not probable.
What are your current test results and what kit did you buy? Do you have one on order from somewhere or only what you got at the pool store? (I'm asking because the pool stores rarely ever sell test kits with the type of chlorine test that is required to do a proper SLAM)
If you are trying to go through the SLAM process without the FAS-DPD type of chlorine test you are not going to be able to get accurate enough results.
You can't halfway SLAM. It's very specific as far as what levels you need based on your CYA.
If you only have pool store results for CYA it's a guessing game for how much chlorine you need to add and what level you need to be maintaining. The result could be a pool that won't clear up because you're not really killing everything as fast as it's growing. In the end you'll end up wasting money on the bleach your adding. (Or, you could get lucky and come up clear)
Rather than gamble with guesses and possibly wasting time and or money, get yourself a kit that has the ability to test CYA (involves a mixing bottle, a bottle of reagent and a tube with a black dot) and a FAS-DPD chlorine test (involves a small container of powder, 2 liquids and a test vial) tftestkits.net TF-100 or Taylor K-2006 (cheaper but with a green pool you'll have to buy refills asap so savings is probably not really significant)
I'm sorry to have to harp on buying something but it's just no good trying to fix something without knowing exactly what you're trying to fix. You've got to get that FC right for the CYA first so that you know you're killing everything.
After you know you're keeping your FC level at or above shock level (Need accurate CYA level for this!), if a few days go by and you see no changes in color or clarity it might be time to look at things to help with filtering (like adding DE to the filter)