Yes, provided the bylaws require directors to be "in good standing" and the board has found the person to be not in good standing after notice of the violation and an opportunity to have it addressed at a hearing. This hearing should be held long before the nomination period ends. It is important that the hearings to determine violations be fair and be perceived to be fair.
If authorized by the governing documents (and subject to satisfying due process requirements), an association can suspend the right of use of the common elements or common areas (e.g. pool, tennis courts, and tot lot) and/or suspend a member's right to vote or otherwise participate in the association if the association acts in good faith and in a fair and reasonable manner. (Civil Code §1366.1, Corporations Code §7341)