By default the service worker does not proxy (cache) POST requests so no, by design, it’s not possible. However… More than one PWA do do just this. As one of the comments says, you need to contact the form plugin author for support.
Reference:
https://stackoverflow.com/questions/35270702/can-service-workers-cache-post-requests
https://developer.mozilla.org/en-US/docs/Web/API/Service_Worker_API/Using_Service_Workers