Sean, think your asking the right questions. Although I'd term it "is he capable" rather than deserve.
There is no doubt he has what it takes to win silverware. Some like to discount it as flukes, or on the backs of great individual players, but he's been consistent in Spain, and now here. You could argue 05 was not his team so he got lucky, but getting back to the final in 07, and the FA cup were his achievements with his squad. The question is can he translate that into a run for the title, which requires consistent performance.
I'll be honest I really don't know the answer. I can understand the many who've questioned Rafa's ability, and have sympathy with many of their arguments. But its just for me too early to decide. Xmas would be the earliest for me, but more likely need until end of Jan or into Feb, which is when I think champions are made.
I never expected a title this year, but of course hoping for it. But I am expecting to know if Rafa is capable of achieving that goal by the end of this season. If he can stay in the hunt until late in the season, then I think he will and should be around next season. With a couple more additions, and the experience the new players this year will have gained over the season, then I'll set the bar that little bit higher on first place. But if he cannot prove he's got what it takes to challenge this year, then it will be time to look around for other options.