It's very imporant! Without the PRV, when the WH runs, the expanding water can actually push back out into the street supply. Water doesn't compress, so that extra volume needs somewhere to go. The PRV has an internal check valve, so now the whole house system is referred to as closed. Now, when you run hot water and replace it with (denser) cold, when it is heated, it expands and must go somewhere. It will go out the weakest link...could be a weak hose splits on a faucet supply, drip out a marginal faucet, damage the hose to the washing machine, or if all those are in good shape, dump water out of the T&P valve on the WH until the pressure is relieved. This isn't normally very much, but will happen any time you run a large enough amount of hot water, close the (say shower) valve, and then that replaced water gets heated.
Add one. It needs to go between the shutoff supply to the WH and the WH cold inlet.