As per the HTTP specification:
If a resource has been created on the
origin server, the response SHOULD
be 201 (Created) and contain an entity
which describes the status of the
request and refers to the new
resource, and a Location header
(see section 14.30).
In a word, no - you can specify a response body and use the Location header at the same time. When using the Location header with a 201 response, you're not redirecting the client, you're just telling it where it can find the resource in future.
Redirects only apply to 3xx responses.
The W3C docs for this explain further, though the text is actually quite ambiguous:
The Location response-header field is used to redirect the recipient to a location other than the Request-URI for completion of the request or identification of a new resource. For 201 (Created) responses, the Location is that of the new resource which was created by the request. For 3xx responses, the location SHOULD indicate the server's preferred URI for automatic redirection to the resource.
I read that as saying "...redirect... or... identif[y]... new resource", but it's not exactly a plain English sentence.