Hi
The color palette for making custom colors is part of Mac OS.
What you called "web colors" are more properly called "hex colors" from the word "hexadecimal" which is the number system used to distinguish one color from another. When you are in the Mac OS color picker, you can enter the "web color" into the Hex Color # box on the RGB Sliders tab of the Colors dialog.

Doing it this way will add your color to the Recent colors portion of the color picker (see picture below).
However, since you are doing branding, there's a whole lot more you can do. I recommend that you learn about Office Themes and Office colors. You can make the color picker across all Office applications have the official colors your organization uses. Here's how the colors for my employer display in the color picker Notice the special section called Custom Colors. That's where you can put your organization's colors, complete with the idiotic names your company's branding department uses. Office Themes can be distributed and even made to be the default for your company's Macs and PCs. The Themes are cross-platform.

There is a web site that explains how all this works:
OOXML Hacking: Font Themes Complete - brandwares.com