Maybe somewhat, but not as much as Poland does, with a “Poland problem” being where a well performing economy does not prevent political unhappiness. Iran is experiencing massive demonstrations that are heavily driven by economic complaints, even though economic performance has improved since the adoption and approval of the JCPOA nuclear deal. Prior to that, in the face of economic sanctions, the Iranian economy was in recession, with GDP actually declining. Unhappiness with this led to the election of moderate Rouhani as president, who negotiated the JCPOA, which led to the end of most, but not all (especially those by the US), of the economic sanctions. As a result, oil exports have risen, and GDP has been growing at 4.5% recently, but it seems that few of the gains from this have “trickled down,” with inflation now rising above 10%. Aggravating the situation is perception of corruption by the ruling clerical elite, who control large portions of the economy through the bonyad
religious foundations. An irony is that many of those enterprises were once owned by cronies of the former Shah with his regime accused of corruption.
This is a very complicated situation, and I think we do not have full information about all that is going on. However, while some of the protests have aimed at Rohani, increasingly some of it has been directed at the top leader, the Vali-e-faqi, or Supreme Jurisprudent, the unelected Ayatollah Ali Khameini, with reports of crowds chanting “Death to Khameini” and burning photos of his face. It also should be noted that while not nearly as deadly as the Green Movement demonstrations against apparent electoral fraud in 2009, they seem much more widespread across many cities in Iran, while the 2009 events were largely in Tehran and a few other largest cities.
It is important to keep in mind how power is held and distributed in Iran as one sees all kinds of characterizations about it, including declarations that Iran is a “dictatorship.” It is not, but it is true that the unelected leader (Khameini) has more power than an elected one (Rouhani). In particular, Khameini is the Commander-in-Chief of the military as well as being in charge of the judicial system based on Shia Sharia, as the proper translation of his official title as “Supreme Jurisprudent” indicates. While he does not directly control them, it is the clerical hierarchy under him, along with parts of the military, that control the bonyads that constitute probably more than a quarter of the economy, which also has indicative planning and a substantial state-owned sector. This latter part is more under the control of the elected president and his economics minister, as well as having more control over the Iranian central bank.