No, pets are not allowed on the building. Nor can they be taken into the restaurant.
However, people accompanied by a guide dog are allowed to access to the building (front desk, shop, restaurant, terrace).
It is important to note that there is an important difference between Alaïa Bay and Alaïa Chalet. Pets are allowed in the bar at Alaïa Chalet, but not at Alaïa Bay.