I believe you can run a 3 (or more) drive RAID 1 array quite happily as you note.
If I recall, the correct way to get from 3 drives to 2 drives is to 'grow' the array but from 3 drives to 2 - I asked the same question on the linux RAID dev list a few years back. Slightly illogical, but that's how it works.
e.g.
If your array has 3 drives that you want to reduce to 2 you do something like this :
mdadm --grow --raid-devices=2 /dev/md1
I do run hot spares having added them manually after install, but there can be issues with grub installing correctly (you really need to test it all works as expected before committing data) so have a read around here and the wiki - try this for instance :
http://wiki.contribs.org/Raid#Adding_another_Hard_Drive_Later (this is wrong for v9 and we need to update the wording according to the release notes
http://bugs.contribs.org/show_bug.cgi?id=8751)
If you have easy physical access you will probably be best to follow Janets advice and keep the 3rd drive in a box ready to go - I usually do that these days unless the machine is difficult to get to or the person on site can't change it easily. Swap drives, resync, no messing with LVMs et al

If the drive IS a hot spare sitting there idly running, I wonder what the stats are to say the minute one drive fails the hot spare decides it is too old and throws its hand in as well ?

RAID 5 on 3 drives ? I know it is possible (saw an interesting discussion on the RAID list once about technically rebuilding a RAID 5 array from one disk, but I think it has a rebuild time measured in aeons !) but personally I'd want a few more drives in the array, though I am not sure what people would advise is an optimum number.
At a certain point RAID 6 or 10 are probably better options. (6 can suffer two simultaneous drive failures, 10 can as well as long as they are not in the same mirror I think)
Again, trade-offs between security and speed as well. Good backups always required

B. Rgds
John