Can Yasuo move a just-played (exhausted) unit to a battlefield and have it initiate a showdown the same turn?

Ruling: Yes, Yasuo can move an exhausted unit to the battlefield, and that unit can initiate a showdown the same turn. Exhausting is only the cost for a unit to move itself; other sources of movement (like Yasuo's ability) do not require the unit to be ready.

Nuances:

• Being exhausted doesn't change how a unit functions; it only prevents the unit from being exhausted again as part of a cost for something else
• This effectively allows Yasuo to give any unit a form of acceleration by moving it to the battlefield immediately