It depends on what you do when you set the mirror up. Assuming you are talking about a 2 disk rootvg mirror then after you have set the mirror up you need to:
1) deactivate the quorum so that failure of a disk is not promoted to a VG failure.
chvg -Qn rootvg
2) ensure that both disks are in the normal & service bootlist.
bootlist -m normal hdisk0 hdisk1
bootlist -m service cd0 hdisk0 hdisk1
3) ensure that both disks have a valid current boot image.
bosboot -d /dev/hdisk0
bosboot -d /dev/hdisk1
4) reboot system so that quorum changes you have made are now active (requires varyoff/varyon of VG and you can't varyoff rootvg with the system up, rebooting does it for you).
If you set it up like this then the system will carry on running if a disk fails, you can then schedule a service outage to replace the failed disk at a more convenient time.