Is someone who studies the judiciary considered to be seeking it, and does the Prophetic Hadeeth, "Indeed, we do not appoint to this position one who asks for it nor one who covets it," apply to him?

Judiciary is a minor form of authority. The Prophet, peace and blessings be upon him, generally prohibited seeking authority and leadership, due to the burden it entails for anyone who does not fulfill its rights. However, if undertaking it serves a legitimate religious interest, such as when the applicant is qualified for it, capable of fulfilling its rights, and intends to uphold the Sharia and bring about reform, especially if no other qualified person exists or if the existing alternatives would cause corruption. Some prophets even sought authority for a legitimate religious interest. Therefore, the general principle is not to seek a judicial position, unless it becomes a necessary communal obligation for a qualified individual, or if one perceives a greater benefit in doing so. As for merely studying judiciary, this does not fall under the forbidden seeking of authority.