To answer that you need to talk to other folks who have that amp & that dac. The best way to do that is to join in a discussion on the relevant thread or threads of the Heaphones Amps (Full Size) section of the Equipment Forum on these boards.
Nevertheless were I you and had $600 to spend, I would buy the HE-500 while it is available at closeout prices ($495 for B-stock currently at Razordog Audio or $539 new currently at TTVJ). I'd put the balance aside for a new (or used) amp that will properly power the HE-500. That will cost no more than $249 (say for a Argard 2) or perhaps much less.
To stay well within your budget get the HE-400 for no more the $299 new. The Alpha Dog may be better, but it currently costs more than the HE-500.