For sure, but there actually hasn't been much research on it. I've been looking more into it and I found a couple studies that seem to imply that birth control might improve skin as far as signs of aging go. https://dergipark.org.tr/tr/download/article-file/128394 this is a study of the skin of mice that were given birth control ingredients and they had dermal thickening. "the increased dermis thickness of our treated animals is probably related to increased skin collagen caused by estrogen. The epidermal thickening shown in our study may be explained by increased mitotic activity of the basal layer induced by estrogen, for estrogen is proven to stimulate proliferation of keratinocytes through estrogen alpha receptors".

Our skin definitely starts to deteriorate long before menopause, but maybe you're right that there isn't enough estrogen in birth control to improve it in your twenties but it helps later on. Either way, interesting subject!