Mention the word "invasion" to someone and you will almost always find a negative connotation linked to the word. An "Invasion" of any kind is met with stubborn resistance and a great push back! However, in it's purest form, I imagine the word simply means "something coming from the outside" - and yes, we usually use the word to speak of bad elements:
But, what if we allowed God to invade? - I mean in a good sense? What if we allowed the Spirit of God to enter into our lives? If you like, to open our hearts to the invasion of the Spirit - coming from outside our world to change us for the good! Wouldn't that be amazing?
And this is what Dallas Willard hints at in his quote (above) - when the Holy Spirit grabs hold of ordinary people and flips their lives around, miracles happen. The early church witnessed this and there is no reason why we can't witness these things again.
Acts 1:8 - But you shall receive power when the Holy Spirit has come upon you;
Living in Grace