Well, sort of. It would depend how the government negotiates the payments given to the companies that provide medical services. If they stick with the standard fee-for-service model we mostly use now, there wouldn't be much difference.
How so? Even under fee-for-service a single payer org has an incentive to provide preventative services so they don't have to pay for problems later, no?
Well, there's two issues. (Two I can think of, anyways, there may be more.) One is that without universal insurance via a single-payer system, there will be people who aren't insured and can't afford preventative services. So, single payer solves that problem.
The other problem is that in a fee-for-service model, health care providers get paid a lot more for major procedures than minor ones, and they may get paid again to fix any complications that arise. So, there isn't a good incentive structure to reward fixing problems quickly and cheaply. Whether single payer fixes that problem will depend on how it's implemented. (I think there was an experiment done awhile back where Medicare stopped reimbursing hospitals for patients who were re-admitted due to infections following surgery. The result was rate of surgery complications went down.)
I kind of wonder if maybe there should be a bounty program for fixing minor problems before they turn into major problems. Just this last week, I had an adenoma removed from my colon. I haven't seen the bill yet, but it was a pretty routine, minor procedure. If I hadn't had it removed, it would have probably become cancerous within the next year or two (according to the doctor that removed it), and if it were any bigger it might have required a much more invasive procedure to remove. So, fixing it now saves a whole lot of medical expenses down the road and saves me a whole lot of unpleasant experiences. It seems kind of a shame that the doctor who removed my adenoma isn't rewarded (except in the knowledge of a job well done) for that.