That alone sounds like an enormous self-defeating ecological disaster, since anybody immigrating from India to USA or from Morocco to France quickly adopts the new, much higher, level of consumption and carbon emission. Nontheless, it is done on a grand scale with very few reservations.
The Swiss ~voted~ proposed a vote on limiting the population number citing carbon emissions. Truth be told the largest groups of immigrants there are Portuguese, Germans and Italians, so if anything it's the other way around considering what kind of energy mix Switzerland has.
That being said I think countries should deal with their population issues on their own instead of relying this heavily on imported workforce.
France was largely successful at keeping their fertility rate only slightly under replacement, so it is possible.
Edit: Can't confirm if the referendum was ultimately scheduled.