Depends on your bank. I've had NAB cards mailed to the branch previously, although this has been a bit hit and miss.
1st time: card got sent to docklands vic, where I signed up for a transaction account, instead of to my residential address in qld which I specifically requested and confirmed with staff.
2nd time: requested the card to be sent to my local branch in qld, it got lost in the system somewhere
3rd time: requested the card to be sent to my local branch, it got delivered to that branch. Third time lucky!