Get a tds (total disolved solid) meter and find out yourself. I have a reef tank so its easy for me since i already have ro/di water on tap.
Tap water reads around 300+ ppm (parts per million) TDS. my water here is 750ppm
RO water brings that down to about 20ppm.
DI resin will bring that down to 0.
Now of your asking for your misting syste. I would say that the hard water over time will plug the misters.
I have extremely hard well water and I use it in my mister. I periodically run vinegar through to keep the mineral buildup down and I haven't had any issues.