Apparently not. An Austalian ABC article says
It is true that collagen, a fibrous protein in the skin, is involved in scar formation and that vitamin E, when present in the body, influences the formation and arrangement of collagen fibres.
But Dr Artemi says it does not automatically follow that applying vitamin E to skin will improve the way collagen is formed and laid down when wounds heal and scars form.
In fact several studies have tested this exact idea and shown it to be false. One study even found that in almost a third of cases, vitamin E caused a common skin irritation — known as contact dermatitis.
I think I found the last study mentioned:
The results of this study show that topically applied vitamin E does not help in improving the cosmetic appearance of scars and leads to a high incidence of contact dermatitis.
In 90% of the cases in this study, topical vitamin E either had no effect on, or actually worsened, the cosmetic appearance of scars. Of the patients studied, 33% developed a contact dermatitis to the vitamin E. Therefore we conclude that use of topical vitamin E on surgical wounds should be discouraged.
The NYT take on this also mentioned that paper and also another study:
One of the largest studies to investigate the claim was published in 1986 in The Journal of Burn Care and Rehabilitation. In it, scientists followed a group of 159 people who had suffered burns over the course of a year, randomly selecting some to regularly apply vitamin E to their scars and others to use a different topical cream. Those in the vitamin E group showed no noticeable improvement in the size, thickness or appearance of their scars by the end of the study.
Which seems to be this study
One hundred fifty-nine operative procedures for postburn contractures of interdigital webs (96), the axilla (46), or the neck (17) were prospectively randomized to be treated postoperatively for four months with a topical steroid (Aristocort A), topical vitamin E, or the base cream carrier for these drugs. The nature of the medication was blinded both to the patient and to the evaluator. Patients were followed for one year. Observations were made for range of motion, scar thickness, change in graft size, and ultimate cosmetic appearance. No beneficial effect of either vitamin E or topical steroid could be demonstrated. However, adverse reactions occurred in 16.4% of patients receiving active drug, compared to 5.9% treated only with base cream. Interestingly, the grafts initially contracted and subsequently grew to be a size larger (about 20%) than the original graft by one year. It is concluded that neither topical steroid nor topical vitamin E is effective in reducing scar formation after grafting procedures for reconstruction for postburn contractures.