The police can only arrest you (for solicitation or prostitution) if they catch you in the act, but there is no such limit on the prosecutor's ability to charge you.  If he obtains strong evidence against you long after the fact he can prosecute you just as if you had been caught with your pants down.  What matters is whether you traded money for sex and not when.  If the statute of limitations hasn't expired you can still be charged.

It is not a crime to be listed in an agency's records.  We all know what being listed there means, but that's not nearly enough to get you convicted.

It may be enough to get the police interested in talking with you, but most likely they would want you to give them information about the agency and the lady you saw.  The prosecutor may even grant you immunity in exchange for your testimony, though you should not count on this.

It is possible that the police and the D.A. will decide to go after you.  This is especially likely if they already have other reasons to want you behind bars.  If they think you're guilty of other crimes they can't prove, they may decide to get you for even a minor crime which they can.

I asked a girl I know, who is an occasional provider, why she worked in a miserable area such as LAX instead of the SFV or Westside or somewhere a little nicer. She said that LE usually left them alone in that area because they had so many more important issues to deal with there, such as all the gang bangers. Maybe? Just her opinion.