Thanks everyone for the info and comments. So if the first was in February and they came every 4-5 weeks after, that puts the fourth series as appearing in stores in May, at least a month after his death.
I did a little more digging. Hodges' card mentions the Jim Fregosi trade on the back, indicating the card would have been finalized for printing no earlier than December 10, 1972. Additionally, Pete Hamm is on card #501 with the Twins; the Twins shipped him to the White Sox on February 5, 1972. Therefore it would seem the cards were finalized for printing somewhere between mid-December and mid-February. Series Five was finalized after February 7, 1972 when the White Sox acquired Rich Robertson from the Giants (he was depicted with the Sox) and before March 19, 1972 when the Sox returned him to the Giants.
Of course, finalization and creation and shipping and release dates are all different things. Being in the card industry as a photo editor, I know cards have to be produced, approved, and ready for print typically weeks in advance of their printing and packaging even now. With 1970s technology and communications, I'm sure it would be even longer.
So for me, that's enough to officially declare for project purposes that it's an impossible card.
For anyone who wants to see the set, it's at
https://www.dfwgrapher.com/sets/1972-topps-baseball (best viewed via computer rather than phone).