I'm Chinese American and when I order garlic shrimp I prefer to eat the little feet beneath the abdomen because it's slightly crunchy and thoroughly marinated in sauce. But I always peel off the rest of the shell since it's hard to chew and usually tough.
A couple of years ago I went to an Indonesian restaurant in New York City and tried a dish where the shrimp had been flash fried in extremely high heat, so the shell was thin, brittle, and edible. The dish was called Nasi Goreng Sambal Udang Petai, or Shrimp with Stink Beans and Rice. I won't go into the unusual beans, which deserve its own StackExchange question, but the shrimp had been fried so that the shell nearly disintegrates when you bite into the shrimp. I found the shrimp shell to be incredibly delicious and ever since then I've tried try to eat shrimp shells if they're not too tough.
So, yes, shrimp shells are edible and may also provide health benefits, like lowering cholesterol and improving cartilidge and joint health.