Hi,
Yes it is possible, you can just let the prices to 0, then do a translation override on the key "FREE_PRICE" in order to replace "Free" by what you want.
www.hikashop.com/support/faq.html#tran
Then set up a payment method, you can for example use the "Check" one and edit all the informations to say "Get an invoice".
This way your clients will be able to add to cart the products they want and create an order. After that you will be able to edit the order, or create order with prices and apply it to the client.