Not at all, in fact here's a small list of countries that have done exactly that: Metric usage and metrication in other countries
Doable? You bet it is.
Australia only switched properly in 1972, and it took only ~2 years for the whole country to complete the transition. That was in the 1970's too, before things like the internet or other easy news networks were even active. If people can organise it over newspapers/radio/telephone then, it can be done now.
