Yes, That's what I mean by going straight from H to e first. The geoid is that conversion.
Although for rtk, the delta isn't to any of the sats, it's to your base station. The deltas to the sats cancel out of the equations, which is where most of the gains in accuracy come from. But it still needs to be tied into a known elevation benchmark.
That said, most field crews will still be shooting a differential to a published benchmark, or plugging the geoid file into the data collector, or dialing into a vrs or cors that already is adjusting for the geoid. For them, H is just an extra data point asking to be plugged into the wrong data field.
Unless you're doing static observations or geodesy or manual network adjustments or direct gravity readings, the new way (22) isn't all that different from the old way (83). There's just different underlying theory of MSL and different math to adjust the network. And if you are doing any of those things, then you generally already know what you're doing.