I've seen this translated as more like 'to your health' and used while drinking. I then understand it in this context, but wanted to confirm that it's only translated insofar as what you say when someone sneezes, not as an actual religious blessing?
You are right. It is widely used as something you say when someone sneezes. But it may be also considered a variation of the toast phrase ("Cheers!") which is usually just "Zdrowie!" in Polish.
We have always said "na zdrowie" for cheers. I have never heard anyone drop the "na" before.