We had a good handful of missionaries that served in my mission (in Japan) that were the only members in their family. One of these elders invited his parents to pick him up. He introduced them to his investigators, some of the members, and some of the other missionaries (and, of course, the mission president and his wife). It helped this elder's parents understand exactly what their son had been doing for two years and really helped improve their opinion of the church. After that experience, our mission president was all for parents coming to the mission.

That being said, our mission was very obedient and parents that came were expected to abide by the recommendations given in the church handbook. My parents picked me up and my dad became my companion. We both wore suits and lived by the white handbook rules until I was released from my mission service once we were back home.