The atmospheric pressure within a tornado plays only a minor role at most in the damage process. Most structures have enough venting to allow for the sudden drop in pressure. Tornado wind speeds increase with height within the tornado. Storm cellars and basements offer the greatest protection from tornadoes. Large hail may or may not precede a tornado.
Tornadoes often follow large hail.
Often tornadoes develop within storms that do not produce hail. Large hail may also follow a tornado rather than precede it. Do not assume you are safe from tornadoes if you do not observe hail. It is important to have access to tornado warning information even when you are asleep. NOAA Weather Radio with a warning alarm device is the best tool to have to be notified when watches and warnings have been issued for your general area of the state.