I have booked flights at the last moment before, but I wouldn't call them mileage runs.
Mileage runs are about maximizing, and while karthik did do a nice last minute mileage run, had it been possible to plan farther ahead, more miles could have been had for less money (taking advantage of those specific promos).
So yes, mileage runs can be done last minute. But the lowest cost per mile cannot be had doing last minute mileage runs.