That's overly simplistic not to mention there are other ways to achieve economic growth other than importing illiterate middle eastern and African immigrants.
It's frankly a terrible idea to simply fill the country with immigrants and then rejoice at the increase in GDP and proclaim the economy is doing better.
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In so many words yes that is exactly what happened. In exchange for oil and resources Europe agreed to allow a constant influx of Arabic immigrants and to allow Islam to spread within our borders.
It's both funny and sad that the supposedly preposterous scenario you outlined is actually the truth except they don't "sit around and plot" like you less mentally gifted people think, it's achieved trough geopolitics.