Yes, Sam. In my culture I hear this phrase often. Usually it is worded, "I am bushed".

It's not a very common phrase, but I think it's still used sometimes. "I'm beat," is more common than "I'm bushed", but you can say "I'm beat", "I feel beat", "I'm bushed", and "I feel bushed".

Australians used to say this, but now you hear people say "I'm stuffed" instead. Previously I'm stuffed" used to mean I'm full and can't eat another thing.