I believe that rooting will hinder your device's ability to install OTA updates until it is back to stock. There are ones who claim it will not affect anything. When I was rooted I wasn't able to perform OTA updates.
Nope! Rooting alone would NOT break the ability to install OTA updates.. BUT you should ensure that you have stock recovery, kernel, radio, rom... If any of these are custom then the sign check fails and so does the update.
Fyi... My phone is rooted but everything else is pure stock and OTA works just fine.