The available evidence seems to me to imply the opposite. I'll stipulate that North America, and especially the U.S., is the global home and font of Biblical Christianity and evangelism by same. But Christianity is alive and well in North America, and increasingly a museum relic in Europe.
In other lands outside Europe, much of the conversion to Christianity is to the non-liturgical Protestant variety (although, to be fair, Catholicism is expanding in Asia, if not as rapidly). But within Catholic Latin America there seems to be a great movement afoot (from what I've read, anyway) into evangelical sects.
Evangelical Christianity is thus growing spectacularly worldwide and taking believers from Catholicism, even as the single place where evangelical beliefs are strongest - the U.S. - is the single place in First World "Christendom" where Christianity is actually vibrant. The author seems to have it backwards, from what I can see.
In the end, even the elect will be deceived. Here's proof.