The original HTTP 1.1 specification says in section 4.3
A message-body MUST NOT be included in a request if the specification of the request method (section 5.1.1) does not allow sending an entity-body in requests.
Section 5.1.1 redirects us to section 9.x for the various methods. None of them explicitly prohibit the inclusion of a message body. However…
Section 5.2 says
The exact resource identified by an Internet request is determined by examining both the Request-URI and the Host header field.
and Section 9.3 says
The GET method means retrieve whatever information (in the form of an entity) is identified by the Request-URI.
Which together suggest that when processing a GET request, a server is not required to examine anything other that the Request-URI and Host header field.
In summary, the HTTP spec doesn’t prevent you from sending a message-body with GET, but there is sufficient ambiguity that it wouldn’t surprise me if it was not supported by all servers.