I've had my Premier card since long before it gave 3x on supermarkets (it originally only gave 3x on 'the broadest definition of travel"). I have other cards that give 4x (year-round) or 5x (quarterly rotating or quarterly special offers) on supermarkets, so I've never used Premier for supermarkets. But I have no other cards that give 3x on hotels. So I use it for hotels for which I don't have the hotel program's own credit card.
But yes, you can earn 3x on gift cards bought at supermarkets. I only tend to buy store gift cars, especially Amazon, at supermarkets. In fact, it's been quite a while since I've paid money directly to Amazon, I just keep using Amazon gift cars I bought at supermarkets. And unlike Visa/MC gift cards, for which there are activation fees, there are no activation fees for store gift cards.