On the one hand, I am not really sure about a direct linkage between the Arab/Muslim Street’s views of Iraq’s nascent democracy and the uprisings across the Middle East. Iraqi's democracy at this point is experiencing growing pains, with so many self-interested actors looking at short-term political gains and sacrificing the future of the nation (e.g. the botched elections that were finally won by al-Maliki). I doubt that the Street is inspired by this kind of phenomena.
On the other hand, it is also callous to dismiss that there is simply no impact of America’s involvement in Iraq on the region. The people must see some positive outcomes in Iraq, such as increased freedoms and openness. They must realize that the type of rancorous debates and critical comments on Iraqi politics just could not happen in their countries; if they did happen, imprisonment, abuse, torture, and so on, would surely follow. And we do know that some Arab reformers wanted George W. Bush to put more pressure on the region’s autocrats, especially Mubarak, to reform or to leave office. But how these things are causally related to what we are seeing in the Middle East, I am not sure.