My recollection is that the plate was wired on. And I don't recall any claim that the explosion caused it to fall off. Instead, it just "fell off" somewhere, probably along I-35 -- as wired on plates are prone to do.
The police officer who pulled him over said the the look of surprise on McVeigh’s face when told he didn’t have a plate was powerfully evident.
There is a theory that he was set up by the muslims involved, who supposedly took the screws out and left one holding it on.
A witness near the Murrah building who saw his yellow Mercury Marquis whip around the corner driving away said that the license plate was hanging by one screw and the plate dangled at an angle due to the centrifugal force as the car turned the corner.