Regarding Depeche, people on Youtube have broken down exactly what each band member was playing during the 80s shows; you might find it interesting. The parts are simple. I don't say that to knock them at all, on the contrary it shows that pianistic excellence has little to do with great synthpop. Alan Wilder is a trained pianist and found little scope for his talents in those shows.
Of course the fast, repetitive bits were either on tape or sampled into the Emulator keyboards.
Good question. Definitely learn the rudiments of piano playing, up to playing block chords (triads) with either hand.
Beyond that, I think they diverge too much. A lot of piano technique is getting both hands working together to play rhythm and melody - but generally synths are doing one thing at a time, and cooperating with other instruments.
A lot of classic synth lines are monophonic, aka "one-finger" lines, although to play them fluidly with one finger would be pretty hard. So pianistic skills would be wasted in this context.
When polysynths got common in the mid 80s, pianistic fingering of chords (but not necessarily rhythms) was used. I mean, to play the melancholy chords of "Drive" by the Cars, you need some of the skills of a pianist, but not rhythmic ones. You do need two hands.
(Of course the DX7 was played very much as a piano at times)
I do think you need the music theory though, such as awareness of chords and functional harmony.
Consider learning some of the classic synth basslines - they tend to have tutorials on youtube - like Material Girl or Tarzan Boy.