I'm not familiar with Lynn White and I'm not a medievalist, but I wholly share Antoninus' suspicion.
White's argument is raising a red flag for me right off the bat. First of all, overpopulation, which is a concept straight out of modern socialism, and something that sounds extremely anachronistic coming out of the mouth of an 11th century pontiff. Urban *may* well have been concerned about sending young men overseas to "keep them busy", but if he was it was concern for the peace in Christendom and not to "thin out" the population. I doubt very much that this concern was even in Urban's mind--unless I see, as Antoninus reasonably requested, some solid documentary evidence to support it.
I've seen in my own studies (American colonial history), how routinely modern scholarship mauls the primary sources to coerce a modern economic theory out of nonexistant historical data. So with all due respect to White (whose work I admit to having never read), I remain extremely suspicious.
No, "Overpopulation" was NOT just a modern concept, especially in the Middle Ages where they lacked modern fertilizers and even a steel plow. The Romans had had a direct experience with "overpopulation" when the farmers, who lost their lands to the plantations, flooded Rome and demanded free bread.