Yes, all H lenses have leaf shutters. But I do not think the 28mm and 24mm lenses work on bodies other than the H4D/H5D bodies. All others work fine on the H1 and H2 bodies.
My understanding is that HCD lenses (24, 28 and 35-90mm) work with H2+CFH back, H2F+CF/CFII back, H2D, H3D, H3D-II, H4D, H5D and H4X (without DAC lens corrections).
The 9 other HC lenses work with all H-bodies.