Although it will be very slow, you will eventually get a cycle with your "dead" rock, as nitrifying and denitrifying bacteria will find their way into your aquarium.
In the freshwater world, fishless cycling has become more popular, and I don't see why it wouldn't work in your aquarium.
Try a Google search on 'fishless cycling'. Basically, you add a bit of unscented household ammonia to the aquarium. You initially test your water for ammonia and nitrites. Once you see the ammonia levels go down and the nitrite rising, that means your nitrifying bacteria population is growing. You continually add a specific amount of the ammonia each day to the aquarium, building up the bacteria population.
After a bit, you start testing for nitrates. When you see them go up, that means your cycle is completing. You will eventually reach a point where you add ammonia one day and it's gone the next, converted to nitrite, and then nitrate by the bacteria.
The nice thing about this is that you get a really good bacteria population built up and you're able to stock more organisms than you normally would following the traditional cycling method.
I'll add my disclaimer here: I've never used this method on a reef aquarium; only freshwater. Since I've always started my reef aquariums with live rock, there was already a bacteria and nitrogen source.
Perhaps someone else here may have tried this or could speak to it.
Good luck!