Looks good in theory, with the high vit A precursors that will work better with the fat(than a carrot) and vit E which is found to be decreased in sebum of acne sufferers.
Anything im missing?
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Big question, are carotenes and tocopherols transdermally absorbed? Magic Google 8-Ball says: "results mixed."
If your acne is caused by vitamin A or E deficiency then maybe..could well be something else though. I assume the carotenes would be absorbed much better than from carrots or other fibre bound carotenes but you still may only get a fraction of that converted to retinol. Give it a go, much worse things to try!