I am interested in your opinion as person for this case and situation.
Well, again, then I have to say, that all of this depends on whether you are looking at this from a criminal or civil perspective.
CIVIL PERSPECTIVE
If you are asking about a civil case, then the issue of consent isn't relevant. The case is a he said/she said and whether or not there was an agreement for the "extra time" to which one side breached the agreement. The threshold question is one of "is the activity legal". There can be no legally binding agreement for an illegal activity.
Rape is not a civil crime. Jail time is not part of a civil crime punishment. The sex worker is not able to prosecute on behalf of the state. The only recourse is monetary damages.
CRIMINAL PERSPECTIVE
If you are asking about a criminal case, then the issue of consent is relevant. The threshold question of "is the activity legal" colors the case. The fact that one person was engaged in sex worker may impeach their credibility on the stand, depending on the legality of prostitution; the fact that there was an original consent; the fact that there is a question about the motives (non-payment for extras); all of these play into and make it more difficult to prosecute.
However, if we take your hypothetical to its natural conclusion, that the activity doesn't destroy credibility too much, AND the police investigation is sufficient to warrant the charges, AND the trial occurs, AND the client is found guilty, AND sentenced to jail time...
then the consent issue is moot. It is a proven that consent was not present for the portion of time that the rape occurred.