I applied for a BVB about 3 months ago and it was granted within 24 hours.
My mother was sick and I supplied evidence of this along with the application so I don't know if that helped at all or not.
If you leave, your BVA will be cancelled but not the actual visa application, that would still be processed but bear in mind, most visa applications applied for onshore require you to be onshore when a decision is made.