They don't have a democracy now, so on that basis the question is moot. However, there is a lot more behind your question so I hope you won't mind my bringing others more qualified to speak to this, able to correct my errors.
The first part "quite gleefully," glosses over a lot of history that led up to the revolution. I won't really go as far back as the installation of the Shah after Mossadegh (sp?) in the early 50s, when the latter was going to nationalize the oil industry. (The coup was, *IF* I understand right, engineered by British & CIA.)
But at least by the 60s there were factions who wanted the Shah out. (I'm relying on the autobiographical "The Hard Awakening" by Dehqani-Tafti, the first Iranian Anglican Archbishop of Iran.) There were at least the fanatic Muslims, and the socialists, and the Soviet Union was in there stirring the pot.
By the 70s the trouble-making was becoming more serious and the Shah started cracking down using SAVAK, the secret police. Matters escalated, unsurprisingly. Then Jimmy Carter pulled the rug out from under the Shah and the revolution got underway.
One of the Iranians on FR recently posted about that time, noting that what the self-professed "mainstream" media showed us was not an accurate image of the time, but what showed best on TV and what was most anti-American. (There being no Internet as we know it there, they had a virtual lock on the news.)
The revolution was achieved mainly by the leftists, the students, who wanted a socialist/communist country. (I knew some of them in college here, '77-'78, and that is definitely what they wanted!)
But that revolution was hijacked by the mullahs. (I do not know how; I hope someone can enlighten me.) Now it is my understanding that the mullahs, and certainly their "enforcer" thugs, are not Iranian but Arab. There's a long dislike of Arabs by the Iranians, I gather, and this just exacerbates the current situation. My Iranian friends tell me the almost all the people hate the mullahs.
There's another factor. Most of the Iranian population today is too young to remember the revolution; all they've ever known are the mullahs.
Look at a couple snapshots, cost of living and demographics (from FarsiNet News:
I think that if the Iranians are able to topple the mullahs, they will have no problem with maintaining a democracy. I suspect it will look a bit more like the Israeli democracy than the somewhat more sedate American practice, but I think they could make it work.