There are several types of "law enforcement officers" under various federal umbrellas. Quite a few, if not most, have very limited powers to engage in "law enforcement." Most of the restrictions have to do with what laws they may enforce, where they can enforce them, whether they have their enforcement powers when they are not officially on duty, and even whether they can make arrests or merely "apprehend."

For instance, absent some sort of special orders or powers, an enlisted member of the military police has police powers only when on duty and on a military installation,and even then, they may only "apprehend" offenders. "Arrest" usually requires a commissioned officer (Yes, I know there are exceptions to this). Even so, they have badges, and some of them carry the badges when off duty--usually against orders.

Maybe some TSO will try and exercise his or her "powers" off duty with the badge, but I don't think they'll get far with it. There are lots of badges out there. Anyone can find an official-looking trinket from a police/security supply company and stick it in their wallet. I've seen some really cool-looking badges that meant nothing at all, from an official perspective, anyway.

The more likely event is that a TSO will flip out the badge on a traffic stop and demand "professional courtesy" on the violation. I have already heard reports of this happening with the cloth badge patches that were/are worn on the old-style TSO uniform shirts. It didn't work very well.