Can an analog Class H still have (would make sense) a switched mode power supply (LOTS of weight saving right there)?
Absolutely. This seems to be what the NAD Hybrid amps are doing, but they have very very little information out in the public domain.
Yamaha's EEEngine amps also have this type of design.
One engineering difficulty about Class H though is the voltage rails have to anticipate the signal peaks. There's some interesting discussions online about Yamaha's implementation, distortion, and fixes. Class G solves this problem by having multiple rails available all the time, but this adds to the possibility of distortion when those rails switch.