[Brian]

One could theoretically write an AppleScript to do that, but I'm not aware of an existing script that does that.

In case it helps, OmniFocus treats items that don't have a Start date/time as having already started.

To be honest, unless you want something along the lines of "I never want to think about a thing I'm filing until a week later", I don't think anyone really needs to assign a start date for everything. (OmniFocus' Start date is really more of a "Don't start this until" date, if that makes sense.)