If you add sorbate to a wine with added sugar or residual sugar plus active, live yeast and do not add campden/k-meta, odds are that wine will continue to ferment until those remaining yeast die off. Sulfites only kill bacteria, and inhibit yeast.
Personally, when backsweetening, my wines are already clear and sediment free, so I measure SG and prefer to add ultrafine sugar until I reach new target SG. Any wine that is being backsweetened is dosed with sorbate/k-meta about two weeks prior to backsweetening. (Though granulated sugar dissolves easily with the help of my drill and stir stick.) The b/s and stabilized wine then rests under airlock for 10-14 days to monitor for refermentation and if any sediment has dropped due to backsweetening, it usually does, it is racked one final time and bottled.