There are two parts to this question. Can you consume APIs from your CRM with the CCX premiums license? Yes you can. However, confirm that it's a REST based API which will be much easier to do. The second question. Can the CCX agent desktop consume APIs from your CRM? Yes, but it depends on what kind of integration you're looking for. The license does not apply here to build a Finesse gadget to integrate with your CRM. However, if you want the agent desktop to be embedded within the CRM then you would need a seperate vendor like Bucher and Schutter to provide a CRM adapter. There are other vendors and you can certainly build your own.
david