Does tenacity reduce GP passive?

Yes. It reduces the duration of the slow affect. However the affect in the case of GP is easily reapplied through auto attacks and his Q. Same goes for Cassio, when inside the slow AOE you get a debuff that lasts maybe 0.2 - 1 second, tenacity will reduce the duration of this but it is refreshed (when inside the AOE) so quickly tenacity will not really affect her slow except for maybe when you leave the AOE and the slow debuff wears off, tenacity will make the slow wear off quicker but since it's duration is not really long in the first place it will not matter too much.

For slows within an area (like Cassiopeia W or Iceborn Gauntlet's field), I believe that the slow duration is continually refreshed while you are in the field, so tenacity doesn't affect the duration until after you leave the area.

For Gangplank's passive, you would have to check if the slow reapplies upon each tick or if the three second slow begins counting from the last application of the passive (AA or Q from Gangplank).