If Anakin didn't show up, Palpatine would surrender to Mace and come up with a plan B or put one into effect. Mace only goes to kill Palpatine after being goaded into it. Palpatine could also do a Force shove, thus allowing him to get up and to try to get to his other saber. Or he could allow himself to be brought to Anakin and try again to get the boy to join him. Or go to the Senate make a case for treason there. Plus, Mas Amedda and Sly Moore are in on everything. All they had to do is work a way for a comlink to get to him, so that he can execute Order 66.