Yes low air pressure in your tires can eventually cause a blowout of the tires when going down the road at high speeds.
The number 1 cause of tire blowouts on vehicles is due to low tire pressure when people don't keep their tires properly inflated.
The low tire pressure causes the tires to heat up faster when on the road especially at highway speeds which then eventually leads to the tire blowout.
You should always make sure your vehicles tires are inflated to the proper tire pressure because driving on tires that have low air pressure can cause a dangerous situation that can severely injure you or your family or cause a fatal wreck.