We do, but you can only trigger those on predefined events, and we want our release manager to be independent of any push or pull mechanisms on the repo. You can also run actions from the github web ui which makes them available even to non technical managers.

Our Action has a single step, it has an "if: false" declaration so it never runs, and no runners are engaged. This immediately completes and fires off a "workflow_job" webhook which triggers the build server to act.