Thanks to both the way the NHS is funded and the way it effortlessly hurls money away, I would be very surprised to find out that is the case.
The average amount contributed to the NHS annually by a UK taxpayer is £4,000, so you'd end up contributing, across your working lifetime, around £150,000 (2016 pounds, of course).
There's not a great many medical procedures that cost that much, even for multiple course and even once you've taken into account the fact that the NHS pays over the odds for equipment and drugs. You might hit it if you've had a few courses of chemotherapy and a liver transplant. And no, the US doesn't have it any better with its insurer-led system that sees similar incredible price-gouging, but then for £4,000 a year out of your own pocket you could have some pretty serious health insurance.
It's a very small and very unlucky number of people who will experience sufficient ill-health to be a net drain on the NHS rather than a net contributor.