The golems take damage
Spirit Guardians states:
when the creature enters the area for the first time on a turn or starts its turn there, it must make a Wisdom saving throw
If the golems are alive when the Cleric enters the room, the golems will take damage if they are within range on the start of their turn, regardless if they are pretending to be statues or not.
What happens after is up to the DM to control the golems
After taking damage they may not react (do golems feel pain?) and could opt to continue hiding. The DM may rule that there is no way to see that they took damage, or the DM could rule that an astute party member could (using passive perception) notice that the spirits seem to attack the statues.
Truesight doesn't help
The rules for Truesight state:
A creature with truesight can, out to a specific range, see in normal and magical darkness, see invisible creatures and objects, automatically detect visual illusions and succeed on saving throws against them, and perceives the original form of a shapechanger or a creature that is transformed by magic.
Furthermore, the creature can see into the Ethereal Plane.
The golems are not in magical darkness, they are not invisible, they are not illusions, they are not shapechanged nor transformed by magic, and they do not exist in the Ethereal Plane.
Truesight is not necessary to detect that the golems are alive if they are alive. If they are not alive, then Truesight cannot detect that they may come to life.