It’s possible but not terribly practical.
The +5V pin on an HDMI connector is required by the HDMI 1.3a spec to provide between 4.8Vdc and 5.3Vdc at 55mA or more. That’s only 11% of the output of a USB 2.0 data port and 3.7% of a USB 2.0 Battery Charging Spec port.
Or, to put that in practical terms, it would take about 60 hours to charge my LG V10 smartphone from an HDMI port. That’s assuming, of course, that I had it switched off because, in practical use, that’s not enough power to offset the power the device is using.
This is why many small devices that plug into HDMI, like Google’s Chromecast, are still powered via USB. There’s just not a practical amount of power available at the HDMI port. The intended purpose of that power is simply to power the device identifier ROM on an attached display sink to allow the display source to see what’s attached, regardless of its power state.