Your question makes sense and "I'd like to have a juice of orange" wouldn´t be grammatically wrong.
Only that "a juice" in the second sentence could lead to ambiguity, because a juice can be the "liquid" from something, from a fruit, etc. So, the other person could just squeeze the orange and give hand it to you. Ha ha ha.
Well, he/she wouldn´t do that if there is money involved, if you are paying to somebody else for the juice, of course. Anyway, it would sound a bit strange.
It would sound as though you get into a bakery in Brazil and order "cinco pães franceses", it would be perfect in a gramatical sense but it would seem to others a bit "unconventional" on your part.http://www.linguabrasil.com.br/mural-co ... 206&busca=
Anyway, no lawyer or cop would drag you to the nearest police station and charge you with attempt to murder the Portuguese language!