The short answer: yes for most of your wardrobe, and the reasons given are half wrong. Velvet hangers do grip, which stops silk and jersey ending up on the closet floor, and they are about 0.24 inches thick against a plastic hanger’s bulk, so you genuinely fit more in. But they are sold on two promises that pull against each other: slim saves space, and slim is exactly what concentrates pressure on a shoulder seam. On a heavy coat the thin bar is the problem rather than the solution. Check the weight rating too, because almost every velvet hanger on the market stops at 10 pounds and a winter coat can be most of that.
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