Yes. I'll describe it assuming there is only one car.
Give the car two move waypoints at the roadblock, close together. In the first one:-
On Activation: player addAction ["Move on!", "move.sqs"]
In the second one:-
Condition: moveOn1
In the script move.sqs
_obj = _this select 0
_man = _this select 1
_index = _this select 2
_obj removeAction _index
player globalchat "Move on there!"
moveOn1=true
exit
That's only a sketch, you'll need to check the syntax and so on.
The car will drive up to the first waypoint. When it gets there, it pauses for a moment as vehicles always do at waypoints. When it completes the first waypoint the action is added to the action menu. When it arrives at the second waypoint (in fact in won't move since they are right next to each other) it will wait until the variable moveOn1 is set to true. This happens when the player clicks on the action and the script is called.