I don't have a 300h, but I do have 0w20 oil in my car at present and it does indeed improve fuel economy by a small amount. I've noticed it after it was put in my car during the last service. It was on 5w30 beforehand.
The engine also seems to react more quickly - spins faster during startup, more free-revving etc, plus idles at a slightly lower RPM.
Supposedly, the thinner oil is also beneficial regarding the hydraulic lifters in the VVTI system.
The downside? It costs roughly twice as much as 5w30! 😃