If the engine went for a few or many years without any oil change, and sat around for another 6 months not running, and THEN you change the oil to a synthetic, you may experience all the crud that has dried up and turned hard being washed down into the oil sump, and then gumming up the suction screen in pieces that were too large to pass the oil pump suction screen and get caught by the filter, this then could cause a "low oil pressure" situation as the pump starved for oil. But this is NOT the fault of synthetic oil, other than it is finally cleaning the crud.
It is kind of like a fuel tank with a bunch of junk, having a fuel system cleaner added that moves the junk into the fuel filter, and so a fuel filter that was OK now experiences being clogged, only a short time after adding fuel system cleaner. You should not blame the cleaner.