I have a webform displayed as a block:
Is it possible to submit the form without refreshing the page, followed by a message saying the webform has successfully been submitted? If so, could someone guide me in the right direction?
Check out Webform AJAX module.
This module adds AJAX support to Webform (3.0 and above).
As a first step it focusses to simply add form AJAX paging and submit. Form submissions get ajaxified including prev/next pages. Especially for multipage forms, this leads to faster loading (less data transfer), better usability and finally smaller server load.
I think that may do what you are asking. Should then show up as options in form settings.
Also, be sure you are set to "no redirect"
There is an option on the block configuration page to "Show all webform pages in block", that will do what you what you need.