I can't speak about Persian, but I can tell you the situation with Chinese: "Standard Chinese" is based on the Beijing-Tianjin accent. However, both cities definitely have regional accents which are quite strong.
My favourite Iranian rapper اشکان فدایی has a very strong Tehrani accent. He sounds more gangsta than Rumi to me!
Well, the short answer is yes it is.
Let me explain in more detail. Due to its socio-political status, Tehrani accent is considered the standard variation of Iranian Persian/Farsi. Persian spoken in Tajikistan and Afghanistan have their own standard versions.
You might ask what is Tehrani Persian. Well, it is next to impossible to find someone in Tehran who is originally from Tehran. Most of the population in the city have immigrated from other cities to the capital or at best they are the second or third generation immigrants. As a result, the prevalent accent in Tehran is an amalgamation of different Iranian Persian accents leveled or neutralized into Tehrani Persian.
Hope the info helps.