You pretty much have it right, there. Live rock is not strictly "dead" coral but there is often dead coral in the conglomerate that makes up "live" rock. There are literally millions of little pores, nooks and crannies in the rock making for enormous surfaces on which the "good" bacteria can thrive and also into which the pods can retreat.
There is a point to getting base rock rather than all live rock and it's essentially that it's cheaper to buy. That's just about the only benefit that I can think of. But any base rock that you put into a new reef with the live rock that you start out with will eventually become "live" rock. It won't, obviously, contribute to initially populating your reef with pods, hitchhikers and...the good bacteria, so while cycling wouldn't necessarily take longer, it would take somewhat longer for the tank to be biologically capable of supporting more fish and an abundance of pods to establish itself. This may well make an algae outbreak a bit more likely than if you start off with a full compliment of live rock since the nitrogen consuming bacteria, which would starve off algae growths, would take longer to develop and adventitious micro-algaes would have the opportunity to start up without competition for the nitrates, so if you mix a good deal of base rock with the live rock when you start out, it's important to be particularly attentive to not overfeeding, doing water-changes regularly, very slowly adding livestock, etc.
