Are you sure the port you're talking about has a REGULAR SATA connector? The eSATA connector is different, but looks pretty similar.
BUT if you are right that the port has a real "normal" SATA connector but is labelled as eSATA, you still DO need the adapter to give you a genuine eSATA connector on the back of your case. Then you actually can plug into it a real eSATA cable to an external unit.
Here's where the sneaky secrets come. Those adapter plates do NOT convert a real SATA port to a real eSATA port. All they do is change the configuration of the connector, without making ANY changes to the signals on the wires. Now, the differences in signals between the two types of ports are partly in small differences in voltages, etc. But there are also differences in some of the logic in the signals and the special functions of the eSATA controller vs. a normal SATA controller. However, the adapters often do the job well or even perfectly. How? Because many mobo SATA controllers actually do most or all of the eSATA functions, but they just don't tell you that. So if you happen to have one of those types of "SATA" controllers on your mobo, the adapter can enable you to use a "real eSATA" port with a mere connector change, because the real work is already being done by the controller on the mobo. In your case, apparently that is exactly what you have, AND Dell kindly told you that.