Update: A nice person at WIPO reminded me of PCT Rule 16.1(f) and PCT Rule 15.3. These rules, taken together, provide that the search fee due is based upon the international filing date, not the date of payment of the search fee. This means that what I wrote in the blog article of a few days ago isn’t right.
The Receiving Office, upon reviewing the fees paid and working out whether any addition fee is due, will (or at least should, according to the rules) check to see whether the fee actually paid ($1372, in my example) matches the fee that was due on filing day ($1536, in my example). If the two fees don’t match, the Receiving Office would mail out a Form PCT/RO/102 indicating that the deficiency ($164, in my example) needs to be paid.
So the trick of filing on February 28, 2017, and paying the search fee on March 1, 2017, would not work. My thanks to the nice person at WIPO who pointed this out to me.