Eh, kinda? Like, you can get away with using tap water. You'll just have a tougher time dealing with algae outbreaks, and you'll still need to dose a dechlorinator like Prime or something.
The whole RODI thing is because corals are finicky little beasts, and if you're tossing water with who knows what in it (nitrates, phosphates, silicates, etc.), you can't exactly control what might be causing them to shrivel up (ex. large amounts of copper or heavy metals in the water).
BUT if you're not keeping corals or other sensitive invertebrates, then feel free to use tap water. Just make sure to let anybody who buys that rock in the future that it was used in saltwater made with tap.
Also: the "live rock" from today is not the same as the "live rock" that most people describe in books. Live rock today is basically any piece of rockwork that has a colony of beneficial bacteria. Live rock typically described in books is rock that has been (hopefully sustainably) harvested from the ocean and still contains a multitude of organisms including (but not limited to) beneficial bacteria, sponges, worms, macroalgae, microalgae, amphipods, and other things.