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You can simulate "Appear Offline" by using Windows Firewall to block Battle.Net traffic. Of course people in your guild and on your server will still be able to find you but realid friends on other servers won't see you. Great for some alone time on a different server if you're in high demand from your guildies.
WARNING: Once enabled you will not be able to change servers so get to the character select screen before enabling this rule.
To do this you:
Open up your Windows Firewall, this will vary depending on your Windows version so I'll recommend you Google that; Once in Winbdows Firewall, select 'Outbound Rules' and then double click on 'New Rules..';
Select Port as the rule type you'd like to create and click next and then on the next screen,choose 'TCP' and 'Specific remote ports' and enter 1119 into the text box and click 'Next';
Select Block the connection and click 'Next';
Ensure 'Domain', 'Priavte' and 'Public' are selected and click 'Next';
In 'Name' put in REALID blocker just to make it easy to know what the rule does and in description type 'Disconnects you from Battle.net and hides you from REALID friends. Once enabled you will not be able to change servers so get to the character select screen before enabling this rule.' and click 'Finish';
After clicking 'Finish' you will see the rule you created at the top of you list and it will be ENABLED;
Click on 'Disable Rule' and it will disable the rule. If done correctly the stop sign will disappear from the left of the name of your rule;
Now whenever you feel the need to go invisible on Battle.NET open up Windows Firewall and enable your rule ONCE you're on your character select screen.