It will create a mini cycle when you add it. I would just go with dry rock so you don't risk any deaths.
It depends what your definition of live rock is. If you mean covered in coralline algae, then yes. But if you mean just spots of micro algae, and small organisms like coepods living inside, then it takes a week or so (if you already have the organisms). The effects of its surface area for filtration takes place overnight.
The die off from organisms going out of the water and changing tanks. Surprisingly some of them can die very easily, especially the good bacteria.
You can just put it in one of those big plastic boxes for storing (I forget what they're called...) and keep similar water as your DT and let it cure. All it needs is adequate flow, a stable temperature, and filtration. This is what I did for the LR in my nano at least. Carey, what have you done?
That filter would be fine.
