Hrm. Well, Alan's never really been out-and-out insane, but he did have a brief episode of "word salad" in canon, during which he spoke in unintelligible gibberish.

Of course, he arrived on the island prior to that episode, so if Del made reference to it, he likely wouldn't know what she was talking about.

Basically, he's a bit on the unstable side, but he's never completely taken leave of his senses.

...and if any of this is too confusing or complicated, feel free to ignore it.