I’m afraid that won’t work, or at least not in the way that I think @peterkroman means. Giving anything a class of “alt” within a paragraph will cause it to use the alt text style and not the alt link color as defined in site styles.
Links only get the alt link color from site styles when they are links with a paragraph that has the alt class.
It may of course be workable solution though if the alt text style is not used elsewhere on the page and can just be set to the color that is required for the alternate link color.