I have noticed an icon in the system tray for Secureline telling me it is disconnected.
This is true it is disconnected because I am not paying for it.
Is there any way to stop the notification from sitting in your system tray if you don’t want to activate this feature?
Avast 2015: Changing, adding, or removing individual program components and features in setup configuration of Avast Antivirus
I see this icon every time when there is no internet connection.
After connecting to the internet icon disappears.
If you follow the helpful link provided by Pondus and uncheck Secureline in the “Tools” column, you won’t see Secureline icon at any time. 
This solution only works with Avast Premire! It doesn’t work for Avast Free!
The images on that FAQ page are from the Premier version. However, the Control Panel > Programs and features > Avast Antivirus - Change - Modify option works for any version of avast.