No.
I understand why this is tempting. But allowing any government abrogation of the right to vote leads to nightmarish issues of abuse. It creates a maxim that is too toxic to allow. Those who score the tests will never be non-partisan themselves, which will create at the least allegations of problems. (And computerization of this process would be no solution either). And the fundamental problem with it is that what the issue at hand is and the actual facts are always in dispute.