Yes, the bacteria will spread just like the higher order organisims, only faster!
If your tank is fishless, the best way to make this happen is to run a fishless cycle, (if you've already done it once before you got the rock, do it again with a double portion of starter organic matter/ammonia source.) When the tank finishes cycling, your rock has a decent head start on it's own biological filtering capacity.
If your tank has fish in it already, it will take a little bit longer, but it will happen. If you're replacing a bioball system with live rock, remove a small portion of the bioballs every week, and the live rock will pick up the slack.
If the bacteria is all you're worried about, either a sample of live rock or live sand will do for seeding your base rock. If your tank is already cycled, then niether is required.