Predicting animal behavior can be tricky! However, cleaners normally will start their tasks right off. And since yours will be coming directly from the LFS, he is propably ready for a good meal!
Additionally, use garlic soaked food to treat your fish. This will also aid in trying to clean up the ick. But I will say, unless this is a very mild problem at this point, the chances of shirmp and garlic solving an ick problem is not good.
If neither works, you will have to proceed with a hospital tank and hyposalinity.
[It would be better if you posted disease problems in the Disease Forum.]
Good luck!