Is Dashboard a separate space on your Mac? This can be configured in System Preferences > Mission Control by changing the checkbox for “Show Dashboard as a space”.
If this is checked and Dashboard is on its own space, Little Snitch can't show a connection alert on top of it (OS X seems to prevent any window to be on top of Dashboard). That would be the behavior you get where you have to switch to the desktop to see Little Snitch's connection alert.
On the other hand, if this checkbox is not checked, Dashboard will show above your desktop and the connection alert should work just fine.
If this is checked and Dashboard is on its own space, Little Snitch can't show a connection alert on top of it (OS X seems to prevent any window to be on top of Dashboard). That would be the behavior you get where you have to switch to the desktop to see Little Snitch's connection alert.
On the other hand, if this checkbox is not checked, Dashboard will show above your desktop and the connection alert should work just fine.