Hi,
Since then, we did some modifications in HikaShop to clear the cache of Joomla when a product is added to the cart or when the cart is modified.
So HikaShop can work with Joomla's caching. However, if the cache is too aggressive, it's possible that you notice issues. For example, if you cache the modules, then the cart module might not be called by Joomla to redisplay itself and thus it will display information which doesn't correspond to what HikaShop has stored in the database.
So I would recommend to configure caching incrementally and test with several browsers that the cart displays the correct information for different browsers.