depending on which drive. If the destination drive - no problem, data will be actually deleted from the source only when the move process is finished, otherwise you may just abort the move. However, if the destination drive is completely broken, there are some tricks how to remove the missing pv: luks - Removing failing drive from LVM volume group ... and recovering partial data from an incomplete LV (with a missing PV) - Server Fault
if the source is died, well, there is end of the story.
Of course it would be more robust, if you would create a mirror or volume with parity.
I have to agree. But adding a LVM signature later to the existing drive if you would decide to use it will be tricky: Moving from Windows to Ubuntu and back