I suppose the gate agent will write up your voucher instantly if he knows for sure he needs volunteers. When lots of people check in from home, the plane can be "known to be full" quite far in advance. Otherwise the gate agent will wait until close to boarding time.
One other possibility is to give you your compensation and you will be gone and then he might offer higher compensation if needed.
In the past 20 years I have never been in a situation where the gate agent was having trouble getting enough volunteers.
Travel tips:
http://members.aol.com/ajaynejr/travel.htm