The eviction is secondary to a unlawful detainer court judgement which the landlord may still pursue for unpaid rent and the direct and legal costs based on you not getting out when you should. The monetary judgment would still be in force even if you get out before it is done and it would show up on your credit and other places.
He's under no obligation to accept rent money from you for the time you are illegally staying and the rent money isn't the limit of his damages by the fact you won't get out.

