Can you save data in PDF Fillable Form via web browser plugin?

[HorsePower Australia]

I have created a PDF fillable form via Adobe Acrobat DC, I have enabled the "Reader Extended PDF More Tools (Fill-in & Save)" option to allow individuals to complete the form in Adobe reader however individuals who download the form from their email via a web-browser i.e. gmail via chrome can complete the form but are unable to save the completed document. Can data be entered into a form using an adobe plugin and saved? or do you have to save the document to your local drive, reopen from that location, complete and then save?