There is no guarantee three CYGSs would yield even one week as #1. Four slams give 8000 points. Nobody under the current ranking system has ever been #1 with as little as 8000 points. Currently Fed has more than 11000, and that with winning only one slam.
If we assume that the same opponent is in all the finals of the majors, that'll yield 4800 points. That means that same opponent will need to win four Masters 1000 a year to overtake the hypothetical CYGS winner. Winning those Masters shields will be a tough ask if the CYGS winner is in the draw plus all the other players who will be splitting the finite number of points available sans the majors. Just look at history and see how many players got to #1 just by winning one or two majors a season; winning three majors virtually guarantees the #1 ranking. The only "realistic" way that the CYGS player doesn't obtain the #1 ranking is if everyone else conspired to have the hypothetical runner up vulture all the points left and the CYGS winner sits out everything else.