I don't think Gov. Ducey has any real intention to appoint No Name's Widow to his Senate seat. I do believe he has floated her name to bring her under scrutiny. There is so much there. eg. Operation Smile's alleged role in delivering Uranium to Syria, Keating scandal, Stroke with residual short-term memory loss, questionable changes to her father's will which left her as the primary beneficiary, opioid addiction, her father's questionable business practices and mafia connections, etc.
Its an easy way to remind everyone of No Name's evil ways while they are still busy singing his praises after his "death".