I don't think so. The shia Iraqi let the Iran shia militant to enter into Iraq and fight ISIS together. During Saddam times, no Iraqi shia are allowed into the armies during Iran/Iraq war. The sunni Iraqi bear all the casualties during the war.Let me explain what is even greater factor than the same sect. Iraqis are ARABS, and Iranians are Persians. And no matter what, ARABS have and always will consider themselves DIFFERENT species to Persians. PAN-ARABISM is embedded in History.
Iraqi shia put religion first, others all are secondary. When Saddam is topple and Iraqi shia put into power, they persecuted the sunni and side with Iran shia.