The order for deciding whether we use a supplemental pick is based on last year's record. But where it affects next year is based on the next year's record. So if the Rams wanted to use a first in the supplemental they would have the tenth pick, so only 9 teams would have an option to pick before them. But the actual pick the Rams would end up losing would be #32, after the Rams win the Super Bowl.
So on the one hand, the team is giving up a pick from NEXT year's draft to get a player for this season. OTOH, the rookie they pick will have missed everything prior to training camp, so is going to be behind the rest of the team, diminishing the value of the pick somewhat.