I think anyone that's done any night (scuba) diving will agree that its amazing... the sea and the way critters in it operate changes dramatically.
Although I've done hundreds of night scuba dives, I've only done a couple of shallow "snorkels" so can't say that I have any experience night breath-hold diving.
However, being less intrusive on apnea, I think one will see even more awesome behaviour and the chance of spearing some great fish will definitely be there as most fish are a lot less wary at night.
To make it enjoyable the conditions will have to perfect and of course one will have to carefully consider the safety aspect of it but I'd say about 80% of the spearing myself and my dive buddies do is in viz between 2 and 5m, so we are effectively diving in the dark anyway. It will also be easier to spot your buddy with a powerful torch than trying to identify his camo-cladded butt in the murky soup we normally dive in.
Dieter, as for the tannemanne.... look they there anyway. Not sure how their behaviour changes at night but as far as I know all the sharks we in the WC have to worry about hunt day and night...so for me....I think my freak-out level will stay more or less the same.
Also, just to make sure there is no confusion - I'm not taking about hunting tail at Bellows in gnarly conditions. I'm thinking more in the line of exploring a spot such as Roman Rock on those perfectly clear and calm days...