I need to process the event when an instance of the certain page type is publishing. I understand that it can be done in the InitializationModule by defining DataFactory.Instance.PublishingPage and casting page type.
But is it possible to process this event not in the InitializationModule?
You can do it from whereever you want, as long as that code is executed before you publish the page. Just think about that if the code is executed several times, you'll attach your event handler to the event each time.