Answer:
If your standings are based on total strokes: Players who do not submit picks for a tournament will show as missing in the cumulative report, and they will essentially be ineligible to win the season-long competition because their stroke total will be far behind other participants.
If your standings are based on winnings: Players will still be eligible, but will receive $0 for the missed tournament.
Note: Commissioners can enter picks for a member after the deadline if needed by going to Commissioner Console > Member Pick Maintenance.