I sense some confusion with terminology here....with "play" and "engagement" being mixed up. As has been said, there should be NO "play" in the fan clutch...as in no wobbling of the fan, at all. That is not the same thing as the clutch engaging/disengaging the fan.
This type of clutch can ONLY fully disengage the fan when the engine is running. When the clutch is not spinning the fan will always be "engaged"...but these clutches do not engage the fan 100% (whether running or not), it'll just feel resistant to rotating when trying to spin it by hand. When the engine is stopped, it just depends on what the temperature was when it was stopped as to how long the fan will spin. If the temperature was high enough to have the fan engaged, then it won't spin much at all...conversely if the temperature was not hot enough to have the fan engaged then it will spin until the silicone fluid "drains" (internally) enough to re-engage the clutch.
There are various levels of engagement, like a standard duty thermal clutch (typically for non-AC applications) that claims to spin the fan at something like 70% of engine speed. Then there is the heavy duty clutch (for AC equipped applications) that claims to spin the fan at something like 90% of engine speed. If you were to spin the shaft of these two clutches side by side, you'd feel more resistance with the heavy duty than the standard duty.
Just remember, the "default" state for these clutches is engaged. It will ONLY dis-engage once the engine is running. To observe this...start the engine up cold and rev it up some, you can hear the fan dis-engage after a few seconds. Or, if you were to start the engine up cold and start driving...usually you can hear the fan pulling lots of air for a few seconds, then that sound goes away as the clutch dis-engages the fan.
Another thing to note..."dis-engaged" is not 100% either. Typically this condition has the fan spinning at something like 20-30% of the engine speed.
There are some good descriptions of how these work on Hayden's site:
Hayden - Fan Clutches and Fan Blades