OK, I'll take a go at this.
Direct answer: NO. Consumer: Get a separate amp. DIYer: read on
I've been mulling over my options for driving my Sennheiser HD-600s for some time. My tentative conclusion is to add a very good headphone driver amp within the spacious Tempest chassis, though that sends me outside the "warranty zone" (hey, I'm an EE, I fix it myself anyway).
Once starting down the "no warranty" path, I'm free to relocate the power switch to the rear panel (where it belongs) and put the headphone volume control on the large left-hand front panel knob.
Having reverse-engineered the Tempest (and Stratos), one of my notions was to utilize a clone of the Tempest's output stage as a headphone amp. I simulated this by driving my Senns directly form the Tempest output. Contrary to my expectations, I wasn't impressed. I will revisit this approach with a breadboarded identical circuit soon, but I found the sound to be somewhat harsh at "get into it" levels. The simple explanation, electronically, is that the Tempest output stage just doesn't have sufficient idle (bias) current to stay in Class A operation when I listen loudly. Further experimentation should reveal more. As for djbnh's Grados, their current demands are way too much for this circuit.
I'm a DIYer, so I'm looking closely at the upcoming PPA v2, MP^3, and an adaptation of the Gilmore Dynalo (
http://www6.head-fi.org/forums/forumdisplay.php?s=&forumid=6), using its own DC power supply sourced off the Tempest's overkill-rated, under-utilized primary power transformer. I'll build these as stand-alones first and then port the best of the bunch into the Tempest case, unless further evaluation/tweaking of the Tempest circuitry shows that to be the viable option that I originally expected. Were I using Grados, I would probably skip all of this and just go straight to the Gilmore Dynalo design.
Finally, don't even think about the Gilmore Dynahi. I have the circuit boards and they won't fit - nearly take the whole case on their own!