Do I need to replace soaking wet insulation resulting from a plugged A/C drain?
Insulation can get wet as almost anything can.  If you can take the insulation out and dry it properly it will be fine - fan and moderate heat.

Insulation itself does not harbor mold quickly.  It is associated with mold because insulation (fiberglass/rock wool) holds water and makes things around it moldy.  As long as you get the insulation thoroughly dry within a few days it does not need to be replaced.