So western society as we know it would falter, but all countries where there is little reliance on industry most people would survive (apart from lack of imported advanced medicines) and in modern countries everyone like re-enactors, Amish, new ager commune people would do OK. So the human race would continue, just not the ultra-modern bits.
Indeed. And even here in the very mechanized rural areas there is more than enough expertise to survive on a 1780's life plan. --- But there would be horrific die off in the first years to a decade.