Don't believe you can without some sort of custom development as it can't be done with substitutions sense there's no field to check against in an IF substitution (onlinestatus field won't report back though such a substitution).

Is it possible then if I only have one group

The problem is profile wise that there is no substitution to check if the displayed user is online or not. So you can use a substitution to conditional display the avatar. You'll need a custom integration to do what you're wanting.

show their Avatars on the fron page when they are online

Don't know how you plan to do this unless you've a module you're displaying users in. In which case you'd need to contact the modules developers concerning this. CB doesn't display avatars for online users in a module; the online module for CB only shows name.