Different player types so it's tough to compare, but I don't think there's any question that her record is in pretty serious jeopardy if Watkins stays healthy.
Freshman years...Watkins is still playing obviously:
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Watkins is a beast, and she will definitely have a shot at this record. I still think it is unlikely for the following reasons:
Clark has a system entirely designed around her creating shots. I am sure Iowa would love to be more balanced, but Clark's scoring skill-level so greatly exceeds everyone else on the team, it would be detrimental to try to force more balance. Will Watkins' team have as great an imbalance, and will she have a coaching staff as willing to go all-in on highlighting a single player as Bluder et. al.?
Clark's usage has gone up each year, but the spike in usage rate and shot volume from her junior year to her senior year has been outrageous. Even as her usage was climbing through her sophomore and junior years, her efficiency (for a guard) was elite and improving. As her usage has skyrocketed this year, her efficiency has taken a little hit, but it is still elite. Will JuJu be able to match that volume without a huge dip in efficiency? Most cannot, Clark is a bit of a unicorn here.
And to that last point, Clark's ability to shoot at high efficiency from 30 feet and in, even off the dribble, even with a step-back, has been the key to her getting up so many shots while still maintaining an elite efficiency. That is the skill that unlocks her game that no one else has demonstrated, and the reason it is so hard to completely lock her down. It is possible that JuJu will develop a similarly unique, unguardable skill like this, but I think it is far from guaranteed.
So if I had to put money on will or won't JuJu break Clark's scoring record, I would bet won't, and I would be pretty confident.
edit: Looking a little closer at the stats Fry posted, look at how much less efficient Watkins have been this year compared to Clark's freshman year (57.5 eFG% vs. 45.1 eFG%)! Iowa has been #1 in the nation in eFG% and TS% each of the last 4 years, and has been #2, #5, #2, and #1 in offensive rating over that span. USC is currently 81st in eFG%, 71st in TS%, and they are 27th in offensive rating. Can they crank up JuJu's usage rate and still maintain an acceptable efficiency? I doubt it.