Wx is not NATS attributable, a fact that was exploited to the full after the last NAS failure co-incided with some less than perfect conditions.
If you decide to make "an unapproved heading change" in bad weather keep in mind that the clear patch of sky you are turning towards is the same patch every other A/C with wx radar is making for. There are no winners in this situation but if you feel you MUST turn tell ATC what you are doing immeadiatley, so, at the very least, traffic can be passed and a small prayer offered up.