I would say the answer to your question depends on your preferred listening levels (as is almost always the case when asking about amplifiers). While the DT880-600s are certainly high impedance, they're also relatively high sensitivity (96dB/mW). That means that, if you want a peak volume level of, say, 100 dB (which is quite loud, to the point where consistent exposure will cause hearing damage), you only need 2.5mW of power. While Schiit doesn't publish a 600 ohm power spec on the Fulla 2, I doubt it's less than 3mW @ 600O, given that it has 40mW @ 300O. You could probably email them and ask them, if you're curious.
That said, if you like to listen at really loud levels, the Fulla 2 definitely won't work for you, because power requirements for volume increase exponentially. You'd need around 8mW for 105dB, and 25mW for 110dB, neither of which I would count on the Fulla 2 would provide. On the other hand, if you prefer to keep things quieter, with peaks around 90dB, you'd only need ~0.25mW, and you'd almost surely have tons of headroom.
Unlike whaiyun, I found that the Fulla 2 drove my HD 650s significantly beyond the volume level I would consider comfortable for consistent listening, to the point that I found myself lowering digital volume just to give myself more range on the volume control. The HD 6xx series headphones have sensitivity around 97dB/mW. If you push the Fulla 2's rated 40mW into that, it's going to produce around 113dB. If you're someone that likes going to rock concerts where they amp everything to an insane level (often around 120dB near the front), then you might enjoy that, but I would consider it a form of torture.
Ultimately, it comes down to your personal listening preferences. If you know you like cranking the volume, I would look for a solution with non-USB power. If you listen at moderate or quiet levels, you're not likely to run out of power with any desktop amplifier.