From looking at my logs (for ver. 2) Nagios only supresses the notifications. The checks still get done, they just have a HARD state type on the first go as the host is down. This means that the event handlers should run. Also from the docs on event handling it seems that the handlers will still run.
The only thing that changes is that the notifications are suppressed. I think this is a good thing as the more notifications are sent out the less likely they will be paid attention to. The admins that I work with understand that if the host is down, then the services it runs are also down, thus further notifications are not needed.