Is Plato's Republic something he wants to see realized or is it a philosophical device designed to spur thought and discussion?
Great question. Obviously, without explicit notes on the subject from the author, this is a judgment call. However, before I share my thoughts on it, I want to make a distinction. Remember Plato's allegory of the cave? In it his philosopher (unchained man) saw the truth (the sun), but when he tried to explain it to follow citizens (those still in chains), he could only explain it in terms of things familiar to them. It was real, but they took it as a story. This fits with his general idea that the realm of ideals is more real than the world of the senses in which we live.
So, is the Republic something he wanted realized? It is already real, and so the question changes a bit. However, that said, if pressed to answer yes or no, I'd say he wants it to spur discussion and thereby nudge society closer to it being real.
Plato's Republic is one which is highly idealised and as a result is extremely difficult to execute. If such a society were to be implemented it would literally require a totally fresh beginning. I think the main point to make here is that it is not necessary to get 'bogged-down' in the literal meaning of Plato's vision. But to be more concerned with the figurative meaning behind many of the analogies and subjects which he is concerned with. Whilst the literal meaning of such a society might seem incomprehensible to the modern reader, many of the sentiments expressed by Plato are revolutionary (relative to the period in which he was working) and most definitely not worth dismissing.