Here is a minimal example of an AppIndicator:
#!/usr/bin/python
import gobject
import gtk
import appindicator
if __name__ == \"__main__\":
ind = appindicat
It looks like the answer is no unfortunately.
print gobject.signal_list_names(ind)
('new-icon', 'new-attention-icon', 'new-status', 'new-label', 'x-ayatana-new-label', 'connection-changed', 'new-icon-theme-path')
I tried all of them and none of them appear to activate when the indicator is clicked. For what it's worth the unity devs seem to want to keep all indicators behaving in a uniform way, so it's quite possible that it's deliberately limited.
There is a bug filed about it on Launchpad https://bugs.launchpad.net/screenlets/+bug/522152
Notice that "activate" signal is available for AppIndicator submenus.