actually many people do not realize that their one month notice takes effect on the date of the resignation letter being tendered but I agree most people would think that they can just offset their notices by using their Annual Leave. It also becomes more complicated if you are working on shift while the HR counts your leaves as per normal working days etc...

well if u already told ur colleagues u will leave they will ask why are u still here ?

if your new company is able to buy your remaining notice period sure then you can leave almost immediately