Yes, a conviction for extortion could clearly be gotten and upheld in this case. Let us look at the definition of extortion to see why this is the case.
The link below defines extortion as follows:
The obtaining of property from another induced by wrongful use of actual or threatened force, violence, or fear, or under color of official right.
The actions of the woman in this case clearly fit this definition. She has obtained property from the men in the form of money. She has gotten it from them by causing fear in them. She caused the fear in them by threatening to charge them with sexual assualt. Even though they never did assault her, her threats could still very well cause fear in them. A regular person would have cause to fear being the subject of a criminal trial. It would subject them to a possible jail term and would certainly hurt their image among friends, family and coworkers.
Therefore, the men would have cause to be afraid and the woman has used that fear to get money from them. This is extortion.