As a general rule, the idea of a GET in REST is that any of your parameters are sent in the URL. As the answer on the question you included indicates, it's doable but misses the point of REST, which is to have a consistent webbish interface. If you want to pass complex data to your endpoint, you probably want to use a POST, which your users will expect to have a body for. I'd highly recommend reconsidering that implementation.
But to your actual question, sure there are clients that can't send a body on a GET. Mostly I'd imagine your clients will be programmatic, say, python's urlib2, and while you can set a body on GET, it is not really the intended use of the module, so you're forcing the programmer to get weird. More importantly, the idea of the REST api is to be client-agnostic, which is why it sounds to me like your API design should be reworked here.
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