Hi,
Yes, HikaShop Starter, as well as the other editions of HikaShop are integrated with Joomla's search system. So you'll be able to configure the HikaShop products / categories search plugins via the Joomla plugins manager and then use the Joomla search module to search through your products / categories.
Note however that for more complex searching capabilities, with dropdowns / checkboxes / radios / etc, HikaShop Business has a "filter" system :
www.hikashop.com/support/documentation/1...-filter-listing.html