Well, while of course some things will only work in Bhutan — like direct democracy, which only works for the Swiss

— the overall idea of
Gross National Happiness apparently has been used, at least on a local scale, on bits of Canada and Brazil (the latter being an unusual country where there are more Buddhists than Jews and Moslems added together!).
What this tends to show is that the idea of measuring technological and social progress in terms of the citizens' happiness, instead of how wealthy they are, is probably transcultural and crosses borders, ethnicities, and social backgrounds. After all, we're all humans

Being somewhat cynical, however, I see that in the West the idea of GNH might be more interesting for countries (or localities within countries) with low incomes and general poverty, below the norm, because politicians can then claim that they're poor but happy. This is pretty much a perversion of the system. Bhutan is, indeed, one of the poorest countries in the world when measuring the wealth of individual citizens; however, what they have is enough to provide them with decent lives. That's why the "poverty limit" is differently set for each country/region. The "perversion" of the system comes into play on a country, say, where the poverty limit is set at $500/month, and a certain region knows that, on average, more than 20% of its inhabitants are below that limit, so they try to apply the idea of using a GNH to evaluate the inhabitants' unhappiness to cover up political failure to erradicate poverty in the region... so I'm a bit wary of politicians using a "happiness index" in the West.
While, of course, in Bhutan things are different. The average Bhutanese lives on a pitiful income which would lead to immediate starvation in the West. But, for them, it's more than adequate for the needs they have. They just have far less needs — and far less expensive things to pay for — than an average Westerner. How exactly to replicate
that in the West, while refraining from collapsing our own systems (which will definitely lead to general unhappiness — precisely the opposite of what's intended!) is much, much harder.
That doesn't mean we shouldn't try