No --- you have it backwards. Verse 14 comes before verse 16. There is no other way to read it --- unless you stand on your head.
Actaully, No. Again. 14 is the fact of the Gentiles coming then James says, this is in accord with the following 1) restoration, 2)gentiles.
v 14 is James' description of Peter's description and not a part of the passage he was quoting, which (again) states that the order of things is FIRST the restoration of david and THEN inclusion of Gentiles.