Not any Italian coach would.
Do you know what was Ranieri's statement for Menez? "He came too young to Italy, he should have played at least 200 matches in France".
In Italy coaches prefer to have older and experienced players, who run a lot and who can defend (which is the saddest thing ever) and it's why Italy will lose a CL spot to Germany. There's no point to hope for coefficients, it will stay like this until they realize that they are still playing in mid 90s.
Giovinco is 'too young' to play and it's stupid as hell.