On the larger question of whether Trita Parsi functions as a lobbyist for the Iranian regime, based on what I know, I'd have to say yes: He has argued consistently against any sanctions against Iran, and an end to sanctions is obviously what the Iranian regime wants. So he is working on behalf of a stated interest of the Iranian government.
If by "the regime" you mean Mousavi and Karroubi, then I guess Jeffrey's right. But if Karroubi and Mousavi are "the regime", then the entire matter of the Green Revolution was utterly irrelevant, right? And yet it wasn't. At all.
On the specific matter of Trita Parsi: I have no long-term knowledge of the dude (and for quite a while thought he was a woman) and have never met him. I just know that when the Dish was covering Iran's revolution, few people were as committed or as devoted to the Greens as Parsi or his organization. To conflate him with the dictators he so actively exposed and resisted and who murdered or tortured people he loves and cares about is just wrong. After the trauma of last June, it's deeply hurtful and offensive.
And Parsi's opposition to sanctions reveals something essential to understand about Iran now: Mousavi and Karroubi, if allowed to take their rightful offices, would almost certainly have been as passionate in defending Iran's nuclear options as Ahmadinejad. In fact, in the latest round of negotiations, Ahmadi may be the most amenable to a nuclear deal - because it would give him some breathing space at home. Mousavi would have been totally constrained as president given the need to shore up his nationalist credentials. That's why Daniel Pipes and many neocons wanted Ahmadinejad to win. Anything else would complicate a policy of isolating, suffocating or bombing Iran to delay its nuclear capacity. And complicate it it has.