A few years ago I had a police scanner wired up at my desk at work and was listening as a series of t-storms was moving thru the area.

I heard a county Deputy report swirling motion in the clouds above the intersection next to my workplace.

We recieved no notification at all of anything all day via the management/security channels even though the NWS had posted Tornado Watches for the area.

Conclusion-
Warnings might be helpful if they are offered but in reality - you're on your own Jack!

(I've found that to be the case in simple workplace safety as well as our Facilities people have endangered many people many times w/o management noticing. When I report the issues I get in trouble.)