Heilberg seems to be an at least decent lawyer, so I'd say an insanity plea is absolutely out of the question; he surely knows how near-impossible it is to get one of those to stick, and that it wouldn't help his client even if it did.
The psych-eval is less to determine Chris's sanity (poor though it is), and more to determine his treatment by the system and possibly some leniency from a judge. The letter both helps him a bit by serving as further proof that this dude ain't all there, and hurts him by his idiotic admissions; I would say that at this point, Chris's best hope is for a plea deal resulting in a bit more jailtime, probation, and sex-offender registry.