But... maybe not true in the sense you intended. Every individual Christian does not have the fulness of God in them at every moment. But corporately - speaking of the church as the assembly - Christians do have the fulness of God in them.
This is also what the verses from Eph 3 you quoted say. You may want to check the Greek to verify, but... if the translator came from the place that I'm from... they would have translated like this:
Ephe. 3:14 For this reason I bend my knees to the Father, 15 to whom every family in heaven and on earth owes its name. 16 I pray that he might grant y'all through the abundance of his glory to be made mighty, in the inner man, with power through his spirit, 17 and that through your faith y'all might have Christ dwell in your hearts with love. May y'all be rooted and established on the foundation, 18 in order that, with all the holy ones, y'all may be thoroughly able to comprehend fully what is the breadth and length and height and depth, 19 and to know the love of the Christ, which surpasses knowledge,...so that y'all might be filled with all the fulness that God gives.
(I think Tarsus might be somewhere near Dallas)