Ehhh. I'm a LEO, but not one from Texas. I'm guessing that this would not be a good idea, unless you have some manner of permit (which I know Texas issues for CCW).
On a tactical level, however, I feel farily comfortable in saying this is a Bad Idea. Think about it for a moment:
1. In order to get the gun into play you would need to exit the vehicle...unless you have some setup with which I am not familiar, or are extrordinarily flexible
2. In most true self-defense scenarios, exiting the vehicle is Not a Good Thing, since you are leaving a position of (relative) safety and placing yourself in harm's way.
3. Unless the law is REALLY different in Texas, one of the first things a DA is going to look at is whether or not you took all reasonable steps to avoid the conflict and/or retreat/escape to a position of safety.
So...if a situation crops up where you would need to use the gun, you will have to stop...place car in park...exit vehicle...reach under seat...remove shotgun...rack...aim...fire.
Thats 1. slow and 2. legally questionable (at best). Better? A handgun (with CCW permit) and training training training.
Mike
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"A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects." -Robert Heinlein