That entirely depends on how loud you are listening and what levels are like on the digital side. Things are not unlikely to be just fine if you are an average to quiet listener though.
A 2 Vrms output should be good for a maximum of 109 dB SPL with the HD6xx, which is well within the green by itself (typical recommendations: >= 103 dB, more conservative >=110 dB SPL). Those who have indicated to require more than 2 Vrms with such headphones have generally been at least middle-aged males, but it probably depends on a lot of factors like what your hearing has been subjected to, genetics and whatnot.
Let's do some math on what that would mean in my case:
I'm using ReplayGain, which is shooting for average levels between about -17 and -21.5 dBFS rms, with a pre-gain setting of -3.5 dB. So here, that would mean average levels between 84 and 89.5 dB SPL, save for a few unfortunate records that would clip and are boosted less (e.g. Mahler No. 4 under Simon Rattle, RG +7.83 dB, true peak 1.000824 - that would see ~4.3 dB less than nominal, i.e. ~80 dB SPL average).
At home, I have my K+H O110 (apparently 95.5 dB SPL @ 0 dBu in, 0 dB) turned down to -6 dB, so with a 2 Vrms (+8 dBu) soundcard output I should be getting ~97.5 dB SPL max. Seems about right, given that my listening levels tend to be about 10 dB below average. I rarely turn op soundcard volume beyond 50% (-10 dB) even on classical, so with the super dynamic Mahler No. 4 that would be... 58.5 dB SPL. Pop might be listened to at -23 dB... 54 dB SPL. That's at 1 m though, while I'm listening at 40 cm tops... so you can probably add another 6-7 dB. My previous guesstimate had been 60-65 dB, so that was pretty much bang-on. That's in a fairly quiet environment, mind you.
So I would say most people should get sufficient output in a combo like that, except for explicitly loud listeners.