I would not call it a "set-up". It is well planned. Nobody can pick on you as long as you do not violate company's policy.
Besides, your boss would see through it anyway.
"Active" at work - it largely depends on what your boss would say, and to some extent how serious HR can be.
THe most tricky day is 30th? If you take a couple of days off after your resignation, usually you still need to come back on the last day to hand over your company assets, some times you may be required to conduct an exit interview with HR on your last day.
There is no perfect solution, take a gamble.