WooCommerce has some compatibility for WordPress caching plugins via the DONOTCACHEPAGE constant, however there is room for improvement. For example, one user reported that "when the website has a shop order and the stock is reduced, the cache for that product isn’t cleared resulting in stale stock levels being used / displayed".
There may be WooCommerce hooks that we can attach to (such as woocommerce_reduce_order_stock) that will improve compatibility with WooCommerce.
This GitHub issue exists as a place to track improvements to compatibility between ZenCache and WooCommerce.