A very complex question for sure. Ty is right though....the nitrogen cycle is forever on going in our aquariums so the question is kinda miss leading to begin with. The real question is how long till the bacteria populations grow large enough to process nutrients through the entire cycle and that question is really hard to answer with out knowing how large the nutrient load will be. If you start with super clean dry rock and sand you may not really experience a build up of nutrients though the cycle. You may be able to add a fish right away (one for a few weeks, and continue adding fish slowly to build up the nutrient load and subsequent bacteria). If you use "live rock" from a store, a lot of time that rock has crazy die off so expect a large build up of nutrients through the different nitrogen cycle stages till the bacteria catch up.
Im with Jordan on the shrimp thing (why a shrimp, could be anything, why not steak), it just doesnt make sense to me. Bacteria grow and die with the nutrient load. Sure you will get some bacteria to grow from adding a shrimp but they will start to die soon after they are done there job. So maybe you could time it perfect and add a fish but really if you needed the shrimp to build up a nutrient load for the bacteria (meaning your tank was lacking nutrients (die off) to build up bacteria) you could have just added a fish and feed it the shrimp (mysis kind preferably).
My suggestion for you (starting a tank with clean dry rock) is to let it sit for a week or two. Test ammonia, nitrite (if you have it) and nitrate (for sure). If you dont see any of these present you are ok to slooowly start adding fish and feeding lightly. Even if you see nitrate below 30ppm you can probably go ahead and start adding a fish.
I hope this made sense. Oh and there is a whole algae cycle you will have to worry about next....always seems to last 3 months for me.
