What about WooCommerce? Can I build and e-commerce on HardyPress?

As long as you use WooCommerce for creating products showcase and catalogs, you can use it with HardyPress.

Unfortunately the “cart” and the “checkout” features can not work on a server-less architecture.  Anyway you can certainly build an e-commerce upon a static website using external services like Ecwid or Snipcart and check if it can fits your needs.