Redoing aquarium, have questions.

Alright so i am redoing my 12g aquarium.  I got thinking I already have a fish in there and 3 corals i want to keep. So i was wondering, if i remove all, or 'most' of the rocks that i don't want and sell them, the same day i go with a bucket of water to a LFS and buy live rock and keep it in the bucket of water, and replace the LR with new LR, it should be cured and not cycle correct? I plan to leave a big ball of chaeto in there while it cycle's so that should help absorb the leftover nutrients and result in me not having to remove the fish and corals. I don't know if i expounded enough, but i just thought of this and i was wondering if it works?

P.S. I would still have the exsisting live sand and live water.

Agreed. Rock that is curing at the LFS may not have a lot of dead or dieing matter on it but it is likely not fully cured, that is sufficient bacteria colonies have not developed to handle the load of a reef tank. Live rock curing in a dark tank with no fish to produce waste that needs to be cycled may look fine but will still require a short cycle to get the bacteria levels up. It's just like adding extra fish can cause a cycle while the bacteria adjust to the load.