Perhaps the opposite will be true. Hypothetically, will all those who feel themselves unwelcome and leave the UK to return to the EU reduce the stress on the NHS and by extension create a smaller requirement for staff.
I am firmly of the opinion that while the NHS offers a valuable service it certainly needs a dramatic overhaul to enable the organisation to function more effectively, in regards to those who need it. I fail to see how an organisation held up to be so wonderful and a beacon for the world to aspire to by so many, in the UK, can be so poor in comparison, generally, to its equivalents in other nations around the world.