Yes, I have experienced bad internet connection before too. If I'm filling a form, when I click "Save" button I would expect it to save, if my connection is bad, it would either say "failed" or the loading wheel of death would go forever which would make me move my computer or phone to somewhere else to get better reception.

Saving to offline storage and sending via service worker when the devices comes back online sounds horrible because there is no way to explain a user that the form they sent will be processed automagically when they are back online.