Yes.
To me it's a must that a person serving on staff at a church be a "member" or at least a regular attender and *gasp* tithes regularly.
Why? Because I'd think it wise to have someone who agrees with the mission and vision of the church, not only Christ's church throughout the world but of the local church, too.
I've already experienced with other churches who hire outside or hire those who have no investment in the church and then either doctrinal differences sever the relationship or commitments are broken because of conflicts of interest or the church is unable to bring Bible-based correction to a person because they exist outside the fold of the flock, even though their life is rife with sin, and if the church tries to bring correction or has to terminate the person, they sue for wrongful termination and slander, etc...
Most churches I'm familiar with have a pretty easy process to become a member. At mine you just come to a luncheon, eat some free food and then sign a membership form if you so desire to become a member.
If you don't, you don't, but don't expect to be getting plugged into leadership of any kind.

To me, being a member of a church where one is working/serving removes any guessing games and hidden agendas between the church and the person.