I was looking to this too. When studying the schematics, it appears that the 5 V bus only supplies IC2, 3, and 4. The rest of the circuit is powered via the 12 V rail which is taken from the input of the 7805. My assumption would be that with an average USB port from a desktop (typ. 500mA capability) this should not cause any problem (provided that putting 5V on the output of an unpowered 7805 will not cause any additional current drain).
Enno,
Somebody did try this recently and said it did not work. But later said it did when powered independently.
I also tried on something, I could not see why, as you say the USBasp's 5V is connected directly to the USB 5V. But I did not check the voltage, just powered it normally.
I believe a USB device reports the current it takes and the computer then might current-limits the output.
I am unsure if it is a good thing to feed 5V to the output of an unpowered regulator.
73 Alan G4ZFQ