Are missions unbiblical?

There are lots of books and resources around on running successful missions and evangelistic events.  Every church does it?  National initiatives encourage us to do it?  Big conferences focus on the need for it?  But as you read Acts you find yourself searching for the idea of a church carrying out Evangelistic events, or having concentrated times of mission in vain.

Don't miss hear me mission is everywhere in Acts, from Peter preaching at Pentecost, to Peter and John in front of the Sanhedrin, to Paul on his missionary journeys.  The churches send people, Philip is known as the evangelist, and so on, mission is everywhere.  Yet that is not the same as having concentrated times of evangelistic activity, such as we often do.

In fact when you read Acts 2:42-47 there are lots of features of the church mentioned yet evangelism isn't explicitly mentioned yet we are told "the Lord added to their number daily those who were being saved."  The church gathering, loving, doing live together, generously and self sacrificially giving, committing themselves to the scriptures, prayer, fellowship and remembering Jesus seems to have automatically brought in unbelievers who were more than intrigued they were fascinated and thirsty for the gospel.

If people are coming to faith everyday there was no need for evangelistic weeks or mission events.  The church didn't need to do mission because they were on mission!

I can't help wondering if having evangelistic weeks or mission events actually is counter productive?  Does it make it seem as if evangelism is something we do just this week?  Or as if this is the service to bring your friends too, and by implication all the others the rest of the year aren't for them?  How do we ensure this isn't the case if we do concentrated mission?  Or maybe better how so we recapture the life being about mission?