I have bought fish in the post on occasions. I've bought bettas, apistogrammas, green neon tetras and endlers (pure bred from registered breeders). I've had two bad experiences - one seller of endlers (not from the registered breeders) didn't use a heat pack and they were all dead on arrival; and the ammonia in the bag of a pair of Apistogramma borelli was very high and the fish in a bad shape, though they did recover.
The rest have all been fine.
Something to bear in mind though is the cost of postage. When I got my fish they were sent by Royal Mail special delivery by 1 pm next day. This is now not allowed. There is now only one courier licenced to transport live fish which means the postage is around £15. This isn't too bad if you buy a lot of fish at once as with fishless cycling but that amount for every small batch of fish is horrendous.
Should you go ahead with this, ask the seller for the hardness and pH of the water he will send the fish in. This will help you know how carefully to acclimatise the fish. Some sellers will be happy to tell you, other's won't. If they don't, test them yourself when you get the fish but bear in mind the pH will be distorted by both ammonia excreted by the fish and the carbon dioxide they breathe out.
The fish will respire in the bag, beathing out carbon dioxide. In a sealed bag, this will dissolve making the water acidic so the ammonia excreted by the fish will be mostly in the ammonium form. When you open the bag, the carbon dioxide escapes, the pH rises and the ammonia becomes more toxic. If the fish need a long acclimatisation it may be helpful to add something to the bag that detoxifies ammonia.
When you open the box, do it in the darkest corner of the house so that sudden bright light doesn't startle and stress the fish.