It's an entertaining idea; but it's pure speculation, with precious little evidence to support it. Most of what Grayling points to just suggests what would have been common at the time -- patronage by courts and the wealthy, and communication among intellectuals on interesting subjects. One of Grayling's odd arguments is that his meeting with Cardinal Berulle somehow suggests that he was an agent for the Jesuits. But this is extraordinarily unlikely; there was clear interest in the early French Oratory in Cartesian ideas as congenial to the order's Augustinianism -- Descartes was good friends with Berulle's successor, Condren, for instance. Further, our evidence is that there was not merely one 'secret' meeting, as one would expect if Grayling were right, but apparently several visits by Descartes to the Oratorian house, plus (even better attested) Descartes's attendance at a salon at which Berulle also attended, at which Berulle asked Descartes to explain to the guests how he intended to fight skepticism. Moreover, Grayling has to overstate rather drastically how intimate Descartes seems to have been with the Jesuits. There are indeed mysteries about Descartes's life; but Grayling's hypothesis, on our current evidence, is conspiracy-theory stuff.
Which is true, but I've been a bit uneasy with my response, because it sounds harsher than it really is, and it doesn't convey just how much of an improvement Grayling's biographical work is over some of his competition. Even on this point, where he makes the same mistake as Richard Watson (no relation), he does so with much more sobriety and reason than Watson does. The Bérulle incident is an excellent case in point. We know for a fact that Descartes had met Cardinal Bérulle: he attended at least one salon that Bérulle also attended; if he interacted with Bérulle outside of this (I should have put this condition in my reply), he likely visited the Oratorian House several times; and, unless I misremember, Descartes name-drops him at least once. Part of the problem in judging just how familiar Bérulle and Descartes were with each other is that most of our sources for Descartes's life are second-hand (Adrien Baillet is the most important of these) and the rest is fragmentary. So there's always a danger of historical pareidolia. We see this, I think, very clearly in the case of Watson's biography. One of the mysteries of Descartes's life is why one of France's foremost minds on a sudden picked up and moved to the Netherlands, there to spend most of the rest of his life. Baillet gives us an interesting suggestion in this regard. Attending the salon I previously mentioned, Descartes interacted with Bérulle, and they were both struck by each other, meeting several more times. Bérulle told Descartes that he should withdraw into solitude in order to write philosophy, and Descartes was so bowled over by Bérulle that he did. Now, this is, I said, an interesting suggestion, but it is not at all surprising that biographers have difficulty regarding this as any more than Baillet's attempt at a 'likely story'. So Watson suggests that really what happened was that Bérulle, deeply involved in the politics of France, tried to recruit Descartes to his cause, and Descartes, repelled by the Cardinal's fanaticism, immediately relocated to get away from him. It's actually rather funny reading it in Watson's Cogito Ergo Sum, since it's transparently obvious that the only reason Watson thinks Descartes must have done this is that that's the sort of Descartes Watson wants to believe existed. It is obviously not any more plausible than Baillet's version, and it lacks two of the merits of Baillet's version -- Baillet, for all that he garbles things, was basing his work on prior sources (the most important of which were Clerselier's lost papers), and Baillet's version fits with the fact that many of the first-generation Oratorians had an intense interest in Cartesian thought. But rather more seriously, we have no serious reason to believe that the interaction with Bérulle had anything to do with Descartes's moving except for the fact that Baillet makes the connection, in the very story Watson rejects as absurd. Without a principled reason for doing this, we are clearly turning history into a wax nose.
Grayling's version has Bérulle, opponent of the Jesuits, calmly letting Descartes know that he knows what Descartes's been up to for them, and (in effect) giving him a choice of leaving or getting in trouble. Grayling's construction of this version is far more sober and less subjective than Watson's (and, it must be said, much more interesting). He takes the trouble to bring in circumstantial narrative; and the result is a narrative much less implausible than Watson's, although one that still raises some questions. The attempt to formulate it is a genuine advance, even if one, like myself, regards it as a dead end, because givent he puzzle it was a possible narrative worth investigating. The admirable thing about Grayling's biography is that he faces squarely a great many of the mysteries of Descartes's life and handle them in a way based firmly on the evidence. I don't think he's usually successful at getting a grip on them, but this has at least as much to do with the state of the evidence as with anything else, and it is a decent attempt.
On the 'spy' hypothesis, it is worth pointing out two things, as well: namely, that to the extent that Grayling endorses the 'spy' label he takes it in a fairly weak sense -- that is, he takes it that Descartes was gathering information, and perhaps trying to infiltrate the Rosicrucians; and that it actually wouldn't be at all implausible for an intellectual of the time to gather information for other intellectuals. It's the systematic and somewhat cloak-and-dagger character of what Descartes would have done that makes it prima facie unlikely of an intellectual in the period; and it sits uneasily with other things we know of Descartes (as I note above, it's very unlikely on the evidence we have that Descartes was so completely involved with the Jesuits as Grayling has to postulate). My suggestion to readers of Grayling's Descartes is primarily that they just enjoy the book; and perhaps take the 'spy' aspect of it as chiefly a literary device that Grayling uses, sometimes to great effect, to lay out the historical background of Descartes's life, Grayling's attempt at a better version of Baillet's 'likely story', and thus to be regarded in exactly the same light we regard Baillet's story.