Not according to Google Translate. They say "Am Prìomhaire" for "Prime Minister". On the other hand they give "Prìomh Mhinistear" for "First Minister". Goodness knows, Google Translate is hardly the oracle. The Scottish government does most of its main headers and so on in Gaelic as well as English so the SG web site might be clearer.
Yes, the meaning is dual. We have ministers in the church and also government ministers. But the context here points fairly definitely to it being a minister in a church. It would be a natural phrase to use if a new minister had been appointed to a neighbouring congregation. In contrast you'd probably only say it in the context of a government minister if you actually worked in a government department and there had been a cabinet reshuffle.
In fact the distinction between "ministear" and "sagart" is the crucial one. "Ministear" would be a protestant congregation of some sort, almost certainly some form of Presbyterianism. It's used by the Church of Scotland and also by the smaller sects such as the Free Church which are very strong in the Gaelic-speaking islands. "Sagart" on the other hand would be a Roman Catholic congregation.
In the "Long Island" (the Western Isles or Eilean Siar) the north, Lewis especially, is predominantly Protestant whereas the south, Barra especially, is predominantly Roman Catholic.