No, sinners don't get to choose when and how to get saved. No sinner will fool God into accepting his claim of salvation if that claim is not based on reality. If Jesus does not first draw the sinner to salvation that sinner cannot get saved, and if a sinner turns his back on the light God gives him in his appointed day of salvation then that sinner will never be able to be saved.
John 6:44
No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.
2 Peter 2:21-22
King James Version
21 For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them.
22 But it is happened unto them according to the true proverb, The dog is turned to his own vomit again; and the sow that was washed to her wallowing in the mire.