The quick answer? No. Is everything the Christian does mission? That is slightly more complicated. But these two issues are addressed by Denny Spitters (vice-president for church partnerships with Pioneers USA) and Matthew Ellison (a missions pastor turned parachurch president and missions coach) in their forthcoming book When Everything is Missions,
It is not too late for the North American church to reassert that missionaries are sent-out ones—to cast aside the notion that everything is mission and everybody is a missionary, or that the debate is only a semantic one. We believe the future health of the Church and the advancement of the gospel in our own context is directly linked to thinking clearly about the mission task and missionary roles. To go and make disciples of all nations and send out those whom God has called for specific purposes is not only a command, it is the very lifeblood of our task—of advancing the gospel and joining in the work of Jesus to build His global Church. (80)
Kevin DeYoung gives a helpful, quick overview of the book and subject here.
I already preordered the book myself and look forward to passing it on to pastors, missionaries, and other Christian friends.