Can OneNote integrate with Outlook so that emails and other items from Outlook can be sent to OneNote?

Yes, there is a button on the Outlook ribbon that allows you to send an email and it's attachments to a OneNote notebook. You can also drag and drop. There is also a way to address an email to me@onenote.com, but that needs to be configured first
Tasks can be integrated with OneNote as well, but calendars, not so much

Thanks for weighing in, Karen.  So is this integration automatic?  Like should I be able to select a plugin or something to see the OneNote button in Outlook?

Automatic, no plugin needed. When you are viewing an email, take a look at the buttons on the Home tab

IF the user has "EverNote" installed, could that be interfering somehow?  I'm not seeing "OneNote" ANYWEHRE.  going to google it to see whereabouts it is supposed to show up.  (I did verify that it is installed on the tablet)

looks like its supposed to be on the MOVE section of the ribbon.  I only see Move and Rules there

OK - so even though it was supposed to be there, Outlook disabled the COM addin, for some reason.  But I noticed the DLL path was in the old Office14 folder.  so I uninstalled OFfice 365 - physically deleted ALL office folders - and then reinstalled Office 365/2016.  OneNote was still not there however, BUT it showed the disabled DLL in the OFfice16 folder this time.  so I enabled it, and all is good now.  Thanks for your help!

Wow that was very odd. So glad you got it to work. You might like to checkout OneNote for Professionals Facebook group. Great place to get ideas

will do.  thanks again! :)