Most boards take USB input @ 5v. So, yes, the ESP can run them directly off of USB, as long as the power doesn't exceed USB power levels. Keep usage under about 2A, and you'll be fine. Exceed that, and the board will go into low power and reset. You can avoid this slightly if you put a capacitor inline with power, but if you draw too much current its not going to help. I have mine running fine off of usb for *months* at a time. See pixelated.cn for some examples.
