Yes and No is the answer to your question. Forget trying to match with SNS NNN. Even if it could be done that type of binding too weak for the job. I assume that you already have an SNS or NNN ski set up that you want to use? If so I'd bet it is too long and skinny for the task anyway.
OK, that's the 'No' out of the way.
The 'Yes' is Silvretta 500 bindings (or variations of). These are ski mountaineering bindings that will take ice climbing boots as well as si boots. When matched to a short wide alpine ski you have a very useable approach ski set up that only requires one pair of boots. For climbing emphasis ski in your climbing boots. For ski emphasis use ski mountaineering boots and climb in them (quite good for steep ice, less good for mixed).