I don't really know what it saves you from.  Maybe you are not prosecuted for soliciting prostitution because the evidence is too weak.  But you won't be walking out of that room free.  Remember, you called and the decoy mentioned a fee if you didn't.  So you have shown intent.  Stings on clients are about publicity to limit the men who consider engaging in it.  So I would think that at a minimum you will get arrested, which is a public record for the newspapers to pick up on after the press release regarding the sting operation.

TER is here so you don't have to worry about performing some LE check.  Use it wisely and LE will not be a major concern for you.  You can start worrying about nosy bellhops instead  

BTW, exposing yourself to a decoy is probably not the thing you want to do.  Depending on the state, indecent exposure may be a worse crime than solicitation.  There was a recent news story from Ohio about decoys in a park asking men to expose themselves and then arresting them.

but it won't keep you from getting arrested. Remember one thing. If LE wants to arrest you they are going to arrest you. It may not stick but the arrest alone could be enough to ruin your life.
The best protection from having to worry about "the touch test" or any other foolish notions about how to spot a cop is to arm yourself with the knowledge that is available here on TER.  Good providers with good reviews do not work for LE.

LE can not engage in any illegal act and further, that LE must tell the truth if they are asked whether or not they are LE.

I must disabuse you on both these notions.

Undercover LE are always allowed to committ illegal acts if same are related to an investigation and by the same token, LE does not have to answer truthfully any question you put to them, unless they are under oath on a witness stand, and even then....

(still not a lawyer)

As for whether it works or not, please see the numerous posts and threads below. Short answer is NO, and it may get you into further trouble.

It may be different in some states that I am not aware of, but in most states, Solicitation by itself is not a qualified offense for required Sex Offender Registration.  However, if you expose yourself, you could be triggering an offense that is. As Trygger points out, LE is using the lewd and lascivious laws, which have more teeth, as a weapon against the hobby.  Typically, the Registry offenses will require something more, like exposure in public or to a minor, but, depending on how the laws are written, you could find yourself with a major issue.

The bottom line, as always, is that if you do your research, you will never be in this situation.

Not only does it not work.  It could be a lewd act in itself. If money had been discussed earlier, you have just done a lewd act for money, or if the touch doesn't happen, solicited a lewd act for money.  And we know what that could be.