Portions of the road are not fully paved. It is regarded as a relatively dangerous road by New Zealanders, and rightly so. Here is an interactive tool that lets you search NZ locations for car accidents; you'll note that there are a lot on SH43, even more significant when you consider how little traffic the road actually gets. If you are not familiar with driving on unsealed roads, or with driving on the left side of the road, I would advise caution.
For the rental, it really depends on the kind of rental company you're dealing with. The big chains that offer you a very new car are likely to be meticulous in checking for damage. The "rent-a-wreck" family businesses who offer you decades-old Japanese cars are likely to be more forgiving, if they even care. And of course there are shades of grey in between.
Indeed, some rental companies have specific rules on where you can take your car, and taking it on an unsealed road may invalidate your contract. Check also your driving insurance. (Note that NZ does not require all drivers to have insurance, which makes it even more important to get insurance as a rental driver. You don't want to ruin your holiday.)
Obviously, people's perception of whether a road is "dangerous" or "difficult" to drive vary tremendously. Let me be clear: The SH43 is nothing like the Carretara 3-NA in Peru, or the Rohtang Pass in India. It's probably more similar to a B or C class road in the Scottish highlands. (Thanks to davidb for that comparison.)