Can I add shortcuts in Microsoft Word like
=rand(34), etc? I'm not sure if these are somehow pulling from a stock VBA script (versus something Word-specific) or how to add more. The MS KB article about them doesn't go any deeper than just saying what they do.
These are Word specific functions (aside from reference in the Word library in VBA from another Office application).
Word VBA does not have access any trappable event for after a user presses return or types a letter (a list of available events as of Word 2003 is here), so unless there is a way with advanced API calls, it is not possible to create your own.
If you don't need to accept an arguement, you can of course create custom AutoCorrect replacements.