As per the subject. I had a client ask whether they needed to install Commerce Server to connect to their retail installation of DAX.
Yes. You have to install commerce server to create an edge catalog between the commerce site and AX. Your website calls commerce runtime services for catalog information and real time services for customer and order information.
Then AX syncs products with the edge catalog via the AX real time services.
Sitecore Commerce is using a "public" API DAX offers and it depends what you would like to achieve with it you can use Sitecore Commerce or you can build your own connector.
Of course if the requirements they have match with the Sitecore Commerce feature set I wouldn't build it my own from scratch. Also learning the API, building the solution, testing and stabilizing, documenting and maintaining your own connector will cost money and the time to market will be much longer meaning the TCO over 3-5 years can be much higher...