Only troops that are produced by a Garrison or Stable under the effect of the Acropolis will have the +15% health bonus. If said troops leaves the Acropolis range it will not lose the +15% health bonus. Troops made by a Garrison or Stable not under the effect of the Acropolis will not gain the +15% health bonus if they walk into the range of the Acropolis.
"Set on a plateau above the Greek city of Athens, the Acropolis is a collection of ancient buildings and monuments famous for their beauty and grace. Built under the guidance of the great leader Pericles at the height of Athens' power, the structures are temples to Athena, the city's patron goddess as well as public spaces, theatres, and the like. The most prominent structure in the Acropolis is the Parthenon, a temple to Athena. The Parthenon stood largely intact for thousands of years until some Ottoman soldiers occupying Athens used it as a munitions dump. In 1687, it was hit by Venetian cannon-fire. The dump exploded, destroying much of the inner structure, but remarkably leaving the exterior columns standing."