"yes, it does... there's some junction capacitance across the diode, and there's current through the diode, both of which contribute to loading of the RF high impedance node. try it on LTSpice, or try it on real hardware."
The diode is not considered as part of the load.
When you talk about "loading" the crystal set, you only consider the earpiece. A crystal earpiece is a very light load and a set of 2,000 ohm headphones is a heavier load. Anything less than 1,000 ohms will not work.