No, definitely not.
The executive and judicial branches must be chosen meritocratically, based on skills.
The executive is charged to carry out the will expressed by the legislature and therefore requires management expertise.
Similarly, judicial appointments require extensive training in the law and jurisprudence.
The primary purpose of sortitional selection of the legislative branch is to insure that the decision-making body can be as close to proportionally representative of the entire population as possible. It is intended to insure that the government is ‘by’ the people as well as ‘for’ and ‘of’ them.