Can you reinstall OS X on a FileVault 2-encrypted drive?

Solution 1:

When you try to run the OS X installer it will refuse to install to a disk encrypted with FV2 and Disk Utility will refuse to partition or erase FV2 volumes.

That being said, if you know your cli-fu you can destroy the partitions using the Terminal app included on the installer (which I've done, although now I don't remember if I used diskutil or just brute forced it by overwriting the partition table with dd, point being that it can be done).

Solution 2:

If you don't care about the data, it's pretty standard (almost doesn't quality as "cli-fu" even); from Recovery HD, you can do it all in Terminal (Utilities > Terminal)

First, do a diskutil cs list to see the CoreStorage information on the volume. Grab the longish UUID of the Logical Volume Group you want to nuke (typically near the top of the output; scroll up). Now, diskutil cs delete UUID (where UUID is the LVG's UUID). Requires no knowledge of the key or an authorized user. Just blows the volume away.

Again, if you don't care about the data. A completely legitimate example of this is a laptop my predecessor used to test FileVault 2. Didn't use an Institutional key or a local one he left where anybody could find it, and his account was the only authorized user.