PostgreSQL: Do regclass/oid columns persist across backups?
I wouldn't rely on the specific values of OIDs to be portable at all. Even if you try it and you find it to work with the current version of PostgreSQL, it might not do so in newer releases.

If you backup your database in a source machine and try to restore it on a different machine (or, in general, another PostgreSQL Database Cluster) that does already have other databases, schemas, etc. it is very likely that the different OIDs your source database was using are already used to represent other different things in the target database.

The schema_name.table_name correspondence to an OID is handled by PostgreSQL within its system tables. If you need equivalent functionality, with the guarantee it behaves the way you need it to and not the way PostgreSQL uses its internal OIDs, I'd recommend you actually duplicate this behaviour with a your_tables table, where you store an arbitrary id (a serial) and schema_name, table_name. This way, your database is safe to backup and restore, and you're likely to avoid modifications for any newer postgreSQL version.

You may need an extra lookup in your trigger(s), but might save you a lot of trouble in the future.