Generally yes, but the wording of "instantly" begs for the following pedantic remark:
This is controlled by jemalloc settings `dirty_decay_ms`, `muzzy_decay_ms`, and their interaction with `background_thread`.
`dirty_decay_ms` currently defaults to 10 seconds, so it's not that instant.
That is important e.g. for single-threaded programs that start other programs, such as my Python example: If it starts a subprocess before the 10 seconds elapse after `free()`, Python (and jemalloc) do not run, and get no chance to return memory to the OS.
In such cases, either enable `background_thread`, or set the `_decay_` values to `0` to ensure immediate return to the OS upon `free()`. (This costs some performance.)
See e.g. https://github.com/jemalloc/jemalloc/issues/2688