I do not see why this could not be handled in OF elegantly, with minor modifications as to the expectations of what it should look like. Of course, the concept of a tickler file was based on a paper office. This requires separate files (43 of them), to track everything. Copying this into the digital office would probably be wasteful.
A tickler is essentially an item with a "due date" and 0 lead time. It shows up the day it is due. How the user handles it is up to them. They can make a project out of it, actually do it; whatever. So a system built around it is not necessary. All you need is a filter setting that groups by due date (already have a framework for that) to view your "tickler file", and for everyday work, a way to filter out items not due yet (set to Available). Using the Context View, ticklers already exist. :)
Although, all of this filter toggling does lead me to hope that there will be an easy way to set filter presets, perhaps in a menu right in the filter bar.
For some people, offloading time-based things into iCal is okay. Personally, I don't like iCal as a production platform, and I really don't like having to go to two places to see what I need to do. I think timing functions are very integral to project flow, and various timing functions should definitely be integrated into OF.