Hi Barry,
I guess you refer to the scenario where your app runs on the HCP local server in Eclipse but connects to a HANA DB in the cloud, correct? If so, then you need the tunnel open - it is actually the connection from your machine to the DB in the cloud.
Please note that both Eclipse IDE and HANA Studio are client tools which connect to the cloud, and there is neither "connection in eclipse to the hana studio" nor "HANA Studio DB" as you have written.
Hope this clarifies a bit.
--Vlado