River Song, land destruction, and brackets

[[River Song]] is a card from the Doctor Who decks with two unique abilities. At the moment I'm interested in the second one: "Whenever an opponent scries, surveils, or searches their library, put a +1/+1 counter on River Song. Then River Song deals damage to that player equal to its power."

There are a bunch of cards that destroy lands, and in compensation, let the controller of that land search their library for a basic land and put it into play. [[Ghost Quarter]] is probably the simplest and best known, but there are 11 in River's color identity and more if we wanted to use a different commander. Normally they're perfectly fine counters for problematic nonbasics like Valakut, but with River, the search now has a downside.

Does putting multiples of these in a deck or a way to recur them count as mass land destruction, which would automatically make it bracket 4?