For other reasons, I'd recommend against.
1) why raise a red flag (sorry for the pun)
2) gmail reads all your stuff and sells the keywords to the highest/best bidder, so your privacy is zippo
3) yes, a good POP3 provider can also reel-in mail from other accounts and become a personal email center.
4) most of the spam I get desiring replies uses gmail, so training them not to respond to gmail users might be tough; they need training in general and you need to do that first and foremost before making decisions about what method you want to use.
5) two-factor authentication is likely beyond their capacity to understand. I'd make this one really simple. Use an auto-updating Linux (like Mint), then setup a menu with few choices. Nothing Windows, and if you send a Mac, be sure it can be supported in their locale.