I just put my live rock into my newly set-up tank with sand. While the tank is cycling, should I start adding calcium to help the rock as well as prep for future corals, or should I wait until the tank is fully cycled?
I agree... and while you wait pick up a calcium and alkalinity test kit. When the time comes that you need to start adding calcium and alkalinity you will need to test the levels before adding the additives.
ALWAYS test before you add anything
I'd allow the cycle to complete before adding any suppliments. Most of the salt products available will have enough calcium to meet normal demands....and with only LR your calcium demand will be low. I'd also urge you to get some reliable tests for calcium/alkalinity prior to adding suppliments....and do a bit of research on the need for calcium/alkalinity suppliments prior to adding them.