Which vendor neutral protocol are you interested in using?
When PGHoard is used in streaming mode it keeps reading new segments from PG and stores them in compressed & encrypted form in a queue ready to be uploaded. The segments will stay there until they can be uploaded.
When using archive_mode PGHoard handles the operation synchronously so PG won't actually remove or recycle the WAL segment in question until the command completes.
Postgres will keep running normally in both cases, but the files will be queued in different places, compressed or uncompressed. This may cause your disk to fill up eventually, but PGHoard will trigger an alart after a configurable number of upload failures.