I've seen reports like this, but they are all anectodal. In addition, I remember seeing similar articles in the past, for example around the time of the start of Schengen, so without numbers it's hard to know what to make of it.

I do have some figures for Israel, though. The Forward, quoting a survey (which I couldn't find) by the Menahim Begin Heritage Center says

A recent survey by the Jerusalem-based Menachem Begin Heritage Center found that 59% of Israelis had approached or intended to approach a foreign embassy to ask for citizenship and a passport.