Usually no. Variant URLs are near-duplicates of the product page, so point them at the main product URL. Google treats rel=canonical as a signal of which version you prefer.
For duplicate or very similar pages, you can tell Google which URL you prefer. Redirects are the strongest signal, then rel=canonical, then sitemap inclusion.
Open a product with a ?variant= parameter and read the canonical tag. It should name the clean product URL. List only the clean product URLs in your sitemap.
Source: Google Search Central, How to specify a canonical URL. Reviewed Sep 23, 2026.