This is what Agile Half-Plate has in its description (straight from the APG Equipment section)
Agile Half-Plate: This style of half-plate is specially crafted in a manner that allows extra maneuverability for some physical activities. The armor check penalty for Climb checks and jump checks is only -4 (masterwork and mithral versions of this armor reduce this penalty as well as the normal penalty). In addition, unlike most heavy armors, the wearer can still run at quadruple speed instead of triple speed.
Most often light armors have no speed penalty, medium armors carry a speed penalty, and heavy armors carry both a speed and running penalty. The special quality of agile half-plate is that it has no running penalty, making it equivalent to medium armor for purposes of speed/mobility.
Mithral doesn't have a special chart to show what effect it has on the armor's speed, it only says that most armor is treated as one category lighter for purposes of speed/mobility. This makes heavy armors have no run penalty, and medium armors have no speed penalty.
What I want to know is: would this make a suit of Agile Half-Plate have the mobility of light armor with the statistics of heavy armor?
No. It would only give the normal benefits. Being agile does not drop the armor into a lighter category, so for speed it does not do anything that Agile does not already do.
Generally, no.
A mithral agile breastplate would work as following:
Armor bonus +8.
Max Dex +2 (+0, improved to +2 by mithral)
Armor check penalty -1 (-4, reduced to -1 by mithral)
Requires heavy armor proficiency.
Arcane spell failure 30%.
Works as a medium armor for abilities etc.
Movement speed as per medium/heavy armor/encumbrance.
Run at 4x move speed (unless run feat etc)
I'm assuming you mean mithral agile half-plate, not breastplate.
Note the -4 for agile is ONLY for climb and jump checks. For swim checks and other dex checks (like riding) you still suffer the full -7 penalty.
==Aelryinth