No. First, there is no such thing as a form that “needs” aria-label attributes – forms needs labels, but the mechanism by which those labels are provided isn’t a requirement. Having an aria-label that doesn’t match a visual label is actually an accessibility violation, so that can be risky.
Second, WP Accessibility only fixes or replaces labels when it can know for certain what the label *should* be; that’s not possible in generic forms. On standard forms, like the WordPress comment form or search form, this is a known value – but on a random contact form, there’s no way to know what the label should be, and WP Accessibility doesn’t guess.
On the site you linked, I looked at the main Contact Form and it has labels; there’s nothing that an aria-label would do to improve those forms.