You can send the postcards in an envelope for protection if you want to, but you do not have to.
Personally I prefer to get a postcard send the postcard way – without the envelope! In that way the postman will get to see it too. And also, the whole idea of mail art is to send it through the mail system openly and spread the power of art.
If yours is very delicate or has chunky bits that might fall of, maybe it’s not a good fit to use that piece as mail art? Design your postcard so that you can send it like a postcard. If you’re unsure wether it will hold going through the mail system, send a trial postcard to yourself first, to see how it holds up.
I agree with artist Lenore Tawney who believed that the cancelling the post office did was part of the design. The book about her work is called Postcard Collages.