Hi Grant
I did this trip a couple of years ago. It was excellent. I didn't have a camera at the time, so I can't speak about the photography of the dolphins from personal experience, but we certainly got pretty close.
Most of the dolphin action is in the first few metres of water, so very shallow. Viz wasn't too bad, probably around 12 metres or so on the day we did the trip. We were quite close in to shore, so if there's been alot of rain prior to the trip, run-off from the land could well reduce the viz.
The way the trips work is that they drop snorkellers off in the path of pods of dolphins, who will either swim by or avoid depending on their mood. The dolphins are more likely to hang around if snorkellers are doing lots of interesting stuff (diving down, spinning around, as much underwater acrobatics as possible really). If everyone just paddles around on the surface, the dolphins will probably just buzz past beneath the group.
As you are trying to get photos, I suggest you try to find the best snorkellers on the trip and stick by them in the water, with the aim of their antics attracting dolphins giving you better shooting opportunities.
One caveat: the swim with dolphins operators in Kaikoura are set up for the tourist trade, and many participants are novices with no prior experience of snorkelling. The staff on the boat may help you with getting your rig in and out, but I probably wouldn't count on it, and your fellow snorkellers may possibly be rather less considerate (or less able to be careful due to inexperience with fins, masks and wetsuits etc) around you and your rig than divers on dive charter boats typically are, so you will probably need to be extra vigilant in guarding your gear at all times. It can be a bit of a dog's breakfast getting into the water! For this reason alone, I would avoid taking strobes just to keep the rig more manageable.
Talk to the operator before you go out - I'm sure they will have had people with dSLR rigs in tow before, and can probably advise you on how best to proceed in terms of ensuring your gear doesn't get damaged, even if they can't offer any advice on whether strobes are a good idea photographically.
Hope you have a great trip.
Another cool thing to do in Kaikoura is go snorkelling around the seal colony there. Try to get out in the morning in late afternoon when the tourist groups aren't there. We went out in the morning (just two of us) and got buzzed by seals quite close in to shore.