shade convertor" cannot get you "ta'hyr, the sun" for free. "shade convertor" allows you to treat your turn as Day, it doesn't make the cards in the center row day.
It's this correct?
The cards in the center row are still night cards. If there is a majority of night cards in the center row and you control Shade Convertor, you may trigger both day and night effect on all your cards.
The only thing it does is let you trigger day effects even if there is not a majority of day cards in the center row. So no, it doesn't get you Ta'Hyr for free.