As far as I know:
- Each lwp will use an object descriptor (a DES) which will sit in the metadata cache. Yes it will have a dbid of 2 assigned to it, but I don't think it'll use any space in that db.
- The plan and sql text will be in the proc cache (the statement cache bit of it where applicable).
- There is no on-disk representation of a lwp as with regular objects/procs (i.e. no sysobjects/sysprocedures entries). They are by their nature non-persistent.
What is it that would use space in tempdb for a lwp?