Certainly competent enough to work it out in the end, yes. As you'd hope with somebody with her academic qualifications. And don't get me wrong, I rather approve of Bayta (partly because she's one of the few characters who doesn't mind-control anyone and doesn't regard planet-zapping genocide as just part of a day's work, but still).

To quote the text, though: "You, Toran, were under control. You never suspected me; never questioned me; never saw anything peculiar or strange about me." Doesn't that suggest that the Mule believed Toran would have figured it out if he wasn't being controlled? The Mule also lists examples of his own suspicious behaviour which are more subtle than using a hyperwave transmitter. My previous comment does suggest I thought that the radio was the only giveaway, which isn't so; I hope I've expressed it more clearly here.