input of class E amp
In a class E amplifier the input can only turn on/off the switch so the (shape of the) amplitude of the input signal does not matter (as long as it is enough to toggle the switch).

The duty cycle could matter as this will influence the amplitude of the harmonics of the input signal. However a class E amplifier has a limited bandwidth, due to the inductors and capacitors. So my guess is that all harmonics will be heavily suppressed. So duty cycle does not seem to matter !

Then what is left ? Frequency ! By changing the frequency you can apply FM modulation. This is useful as almost all High Frequency / RF amplifiers are used for FM modulated signals. 

And indeed class E amplifiers are used for RF / High frequency applications.

So you could feed the class E amplifier a sinewave, however if you would feed it a squarewave with the same frequency, the output of the amplifier should be the same.