No. The Q (and Q) have been pretty well explored in the previous shows. Q bookended TNG, we saw Q politics, we saw the Q explore reproduction and death. The show will only have 10 episodes, so I'd rather not have character X or character Y in it just because they used to be in TNG.
At the very end, whenever the show ends, in a coda scene, where they have a short talk like old friends...
If they do use Q, I wouldn't want to see him be as chummy as some here have suggested. Q works because he's Picard's gadfly. If he assumed the appearance of old age, it would be to mock Picard, not honor him.
I think it would be important from Picard's characterization standpoint to show the effect Q has had on his current choices. He knows Q is always watching him, for better or worse.
^ He covered that in "Farpoint": "If we're going to be damned, let's be damned for what we really are."
^ That was the Picard of Starfleet and its ideals. How does the Picard post-Starfleet see himself with regard to his past and his gadfly Q?
^ Ordinarily, no. But when faced with a huge life choice (of leaving Starfleet), he might think about the tapestry of his life and wonder whether he is making the right choice or not.
I'm 50/50 on this one. I didn't vote as a result because I'm truly torn. I love the Q character and he had some great moments in TNG/DS9 and even Voyager. The novels have of course featured further appearances by Q (though it's questionable whether they will survive with the nu-TNG show). But I don't want it to be some fan lip service episode where he's just brought on because they think it would look 'cool'. But I wouldn't rule it out either. If done the right way, Q episodes can be great episodes. And yes, I wouldn't recast Q. If it's the Q we all love, no one does it better than deLancie. His age wouldn't be an issue for me--there are millions of ways to explain his looking older--mocking an older Picard is just one of many good explanations. I wouldn't sweat that or make that the only reason not to put him in.
Maybe in the final scene, have Picard sitting with someone who may or may not be Q, so we can debate it endlessly on here.