ANSWER: Yes, for sure. If your website uses another application for its homepage i.e. Shopify, Magento, etc but you wish to keep a blog separate, LittleBizzy can host your blog as a subdomain such as blog.example.com completely independent from your other website (homepage).
However if your homepage is WordPress already i.e. WooCommerce we strongly encourage you to keep your blog as part of that install for SEO/etc reasons. It is much easier to manage things as a single WordPress install than having unnecessary extra installations of WordPress to deal with.
If you are going to be swapping your homepage for another software and wish to CHANGE your blog to a subdomain we can do that too (best to discuss with us first). We will probably have you order a Domain Syntax order in that case.