Yes, but he takes any remaining Armor Check Penalty as a penalty to all of his Str and Dex based checks.
A character who wears armor and/or uses a shield with which he is not proficient takes the armor's (and/or shield's) armor check penalty on attack rolls as well as on all Dexterity- and Strength-based ability and skill checks. The penalty for nonproficiency with armor stacks with the penalty for shields.
Full plate has a -6 ACP and mithral reduces that by 3. So he would take a -3 to all attacks, all Str and Dex checks, all Str and Dex based skills like Climb and Acrobatics, as well as initiative due to it being a Dex check.