So, in investigating meditation, I've learned that the needs freeze is totally random and a very low chance. Not to be relied upon. If it happens at the beginning of a meditation session, it will persist for quite some time and possibly until stopped. It doesn't seem to ever kick in mid-session.
When this occurs, moodlets will also stay. You can tell if this is in effect by watching a positive moodlet that would normally be decaying. If the duration goes up, their needs are likely in a reduced decay state (needs testing) if the moodlet now states no duration, they are in a perfect state and needs will not decay. The Sim is zen and leaving the world and its troubles behind, so when they have finished they are in the same state they were before, minus any negative moodlets which decay normally.
So I guess I can say that this doesn't have a major impact on gameplay as I'd hoped. I've been doing tests and find the need decay chance is probably at or around 10%, given that I've had about 30 tries and only seen 3 successful freezes.