I would argue that on balance, Pershing Square has benefited from being promotional (plus being large shareholders). And whether their picks were right or wrong, the market has been rather quick to agree/ disagree.
I would also argue that PS's holdings for the past two years skewed towards compounder-type businesses (that were never really "value" on an absolute basis even when taking into consideration their asset-light nature), and for the most part already had considerable marketing heft within the enterprise. And because they benefited largely from the large-cap/ compounder trend, there really was no need to go out to the media touting XYZ position.
Were the inverse true, I would wager they would not be sitting quietly.