Will this screw up Nvidia web driver?

If the update changed the build number then updated Nvidia drivers are likely be required. Nvidia has not issued any new Web drivers yet.

[Link Edited by Host]

Update specifically what and from what version to what version?

Yes, Apple Security updates change the macOS build number so this does mean you need to update the Nvidia webdriver to match the newer build number. Nvidia have issued an update already for this for the High Sierra update.

There is still at this time no Nvidia webdriver available for Mojave.