Then by your comment it would be just as accurate to say the Holy Ghost or Father chose Mary as saying Jesus chose Mary?
If it were worded under the same terms as the original question. The claim was that Christ did not choose His mother. I gainsaid that because of the nature of the Trinity. The words and the context of Luke say "God" as in the complete Triune God. Christ, as part of the Triune God certainly could be said to 'choose' Mary. The actions of Jesus on Earth are not the actions of the Father or the Holy Spirit because of the context and because Scripture differentiates between the Incarnate Jesus and the Father and the Holy Spirit at that point.