It depends on how they navigate back to the view. If they browse to the view, then change a quick filter, then go back to the tableau content screen and pull the view up again, it will not reflect the changes the user made.
but you will notice in Tableau Server 8.1 that when a view is loaded a session number is appended to the URL, like this:
If you take that view's URL including the session id (#1) and paste it into a browser, the quickfilter changes will be reflected.
There is also a "Remember my changes" option on views in Tableau Server that creates a custom URL to keep changes to quick filters and such.
If you set a date range filter or multiple select list filter to the desired default(s) and then publish the view to Tableau Server, the filter will remain as configured when a user loads the view. Making this adjustable to the user is as simple as making the filter a quick filter.