Can text boxes be set to NOT print?

For instructions that are actually in the body of the document, the closest you can get in Word is to mark the instructions as Hidden text. Then turn on the option to display hidden text on screen and turn off the option to print hidden text (both of these are on the Display page of the options dialog).

These option settings are specific to one computer, so this method isn't appropriate for a document that will be shared to multiple computers. To do that you'll need some macro code. One way is just to use macros to set and restore the options when the document is opened and closed. This will do it:

Dim ShowHidden As Boolean
Dim PrintHidden As Boolean

Sub AutoOpen()
    ShowHidden = ActiveWindow.View.ShowHiddenText
    PrintHidden = Options.PrintHiddenText
    
    ActiveWindow.View.ShowHiddenText = True
    Options.PrintHiddenText = False
End Sub

Sub AutoClose()
    ActiveWindow.View.ShowHiddenText = ShowHidden
    Options.PrintHiddenText = PrintHidden
End Sub

However, the printing option will remain set to False as long as the document is open, and any other documents that you print during that time also won't print any hidden text they contain. That may or may not cause a problem.

As long as you're working with macros, you can use another method to display the instructions in a message box (if the text is fairly short) or a userform (if it's longer). For instructions, see http://gregmaxey.mvps.org/word_tip_pages/custom_vba_msgbox.html. Because such a message isn't part of the document body, it naturally won't print. You could also provide a Quick Access Toolbar button to let users display the instructions at any time while they work on the document.

Actually, you can hide an individual shape by using the Selection pane (Home tab | Select | Selection Pane). Click the little "eye" icon on the right.