No, I believe strategic resource dependent units will function at half strength until the available quantity of a particular resource is restoredgreater than or equal to the number of units that depend on it.
From Civ 5 wikia site - Resources:
On the other hand, if the civilization loses access to some of the strategic resources they are currently using, and find themselves using more than they're producing or trading, then military units depending on the resource in question will fight with a large combat penalty, until the situation is remedied.
This 2K Forum post seems to confirm that it can bethe penalty is 50%:
Sometimes I see enemy units feature a -50% strategic resource penalty in combat.