OTA updates are usually patch-style updates. That means the whole file is not shipped, just the differences from the previous file. Sometimes if the update is major, they will ship the update with the complete files.
The OTA updates will download to your phone regardless of whether you root. What will stop them from downloading is if you stop the process from checking or you change your signature to look like you already have the update, but rooting by itself will not affect those processes (though you would root your phone to make the aforementioned changes)
Now once the process determines you need an update and downloads the update, then the file gets sent to the recovery process to install.
If it is a full update, then it will just blast over any changes you made and it will normally succeed, even if you have made changes.
If it is a patch-style update, then it will first verify that the SHA signatures of every file/partition it is patching are original and unchanged. It does this because if the files/partitions are changed, the patch will not work and worse, would produce gibberish if the patch was applied without the verification.
So the answer to your question is it depends. If you only add root, you are just adding files to the system, so all the SHA signatures will pass and the OTA update (both full and patch) would succeed, though in the process of running the update, it resets all the permissions in the directories, so you would lose "root" capability, though the files used to give you root are still there (in the patch style update)
However, often if folks add root, they are eventually tempted to change some original OS files, in which case, the patch-style update would fail.
Incidentally, you normally don't need to worry that rooting your phone and changing files and subsequently having the OTA update applied by accident will screw up your phone. The patch-style OTA update will first verify all the files are original before making a single modification and if you have changed files (it depends on) the OTA update will just fail. That's not to say you couldn't artificially create situations where an OTA update will screw up your phone, but it normally wouldn't happen.