If you have www.siteaddress.com as your primary domain then that means that your SSL certificate is applied to that domain/sub-subdomain combination. Normally the non-www URL will forward to the www URL, but not if you explicitly add the https before it.
So here's a break down. What happens if you type the following into your address bar:
- www.siteaddress.com - forwards to https://www.siteaddress.com
- siteaddress.com - forwards to https://www.siteaddress.com
- https://www.siteaddress.com - nothing, this is your default address
- https://siteaddress.com - You get a security warning because SSL is not applied to this domain.
Just make sure you don't ever link to https://siteaddress.com. Otherwise you should be okay, the only way someone would get that security warning is if they type in your domain, without the www, and WITH the https prefix.