Here in the UK, most modern fire alarms do not use traditional bells but use electronic sounders that can be programmed to emit various sounds including a passable electronic imitation of a traditional bell.
I presume that USA fire alarms are similar.
It might therefore be worth use of an alternative sound on an existing fire alarm system to give the tornado warning in schools or large workplaces.
This would be especially useful in districts equipped with tornado warning sirens but where the sirens may not be reliably heard in a large complex. It would be a simple matter to trigger the tornado warning when needed for practice purposes or for a real tornado.
(I know that this is an old thread, but having recently been testing a new fire alarm system, it got me thinking)