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This is a common question, here is what is usually the issue, whether or not the police engaged in "outrageous conduct" to entrap the accused (defendant).  This can get complicated, but the focus is upon whether or not the accused had a pre-disposition to commit the crime.

Usually it is something like a task force finds child molesters who advertise for an underage girl.  The police make contact and send over an underage girl to meet the guy, then arrest him.  That is legal.

You are concerned with solicitation, well yes, the same type of thing can be used.  You were going to commit the crime anyway, just needed a customer.  They supplied a customer and you are busted.  The same goes for the customers set up by decoy cops.

A more interesting question is what happens if the cop actually has sex with the girl.  Well, there is some law that could permit that.  But no DA is going to prosecute the case when the testimony, and video tape, etc., shows the copy actually getting a blow job.  But the girl is still going to be charged, and probably will plead to something, etc.
Remember it is very common in durg cases for actual drugs to be "sold" to "defendants". I don't see why sex can't be given either, execept for that Outrageous conduct defense.