OK to put temp tablespace on volatile storage or to omit it from backups? (Postgresql) I would intuit that it's fine, but I just want to make sure there are
no gotchas from a recovery point of view:

If I were to lose my temp tablespace upon system crash, would this
prevent proper crash recovery?

Also, if I were to omit the temp tablespace from the base backup,
would that prevent proper backup recovery?
If you are referring to the base/pgsql_tmp, then you should be fine. But I don't speak from experience of having done that myself. The only gotcha is that you have to make sure that the location is accessible when your PostgreSQL server starts up.

(Ref.: Book PostgreSQL 9.0 High Performance, page 93).

The book in question refers to creating a simlink of the base/pgsql_tmp on the OS partition or other less "safe" partition (i.e. non-RAID or the like).