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Probably not. You'll want a desktop amp for the HD600, since it is a very power-hungry headphone.
I believe Boomana has a guide for newbies, which states a rule of thumb regarding amplification: desktops > portables, as proven by continued existence of desktop amps (i.e. if portables were that good, one would expect desktop amps to be wiped out of existence).
WoahReQQuiem: I have a friend who runs her 650/600 (can't remember which model she has) unamped. You could probably do the same and save up for a decent, entry-level amp. Maybe the Fiio E9?