Yeah. Yet, they need to find a national identity. If they haven't formed one after half a century, they will never be able to form one. Many other countries have become sovereign nations in Europe and Asia and almost all of them have been able to form their own identities. Look at Eastern Europe or the Caucasus for example.
Shi'ism does not play a role in the Iranian identity. The Iranian identity that unifies Iranians is based on Nowruz, the Yalda Eve, the Persian Literature (Hafiz, Khayyam, Mowlana, Sa'di, Ferdowsi, etc.) and the Iranian history from the Median Empire to the 1979 revolution.