Will ‘private’ status prevent Woocommerce products to be indexed by search engines?

If you are using the default WordPress method of marking a post/page private, NO. This only prevents that post/page content from being viewable.

Google (and other search bots) will not find private pages. Only logged in blog Editors and Administrators can see Private pages.

So, while WordPress will not add the meta to block bots, your private pages still will be invisible to Search Engines.