Couple of options,
1) If the rest api is going to provide you only one record for a given input/inputs, you can use the BES-external-calls and map it accordingly to the business entity on the writeCO. So the data provide by the REST Api and the entered by the user will be saved into MDM at the same time.
2) DaaS lets you view the records on a pop-up for the given input. The user can choose any record and import into MDM. The one you are referring above is DaaS. If I am correct, DaaS can be configured in MDM as only a SOAP. You can wrap the Rest API to produce a SOAP webservice and configure accordingly in provisioning tool to import the data.
Please let me know if you have further questions.