To one of the posters: yes, some new mobo's have eSATA ports built in. Mine does - ASUS A8R32-MVP Deluxe with a Silicon Image controller. Actually, it has two SATA controllers, in a way. The southbridge provides both 2 IDE ports and 4 SATA II ports for internals. The Silicon Image extra controller on the mobo provides one internal SATA II and one eSATA port.
To OP: eSATA controllers are SURE to provide a couple of features of the SATA design that are not always implemented in internal SATA controllers. These include, particularly, support for hot-swapping. So you can do what you propose - just run a cable from an internal connector from the existing sATA controller out to an external enclosure. It will work, BUT it may or may not give you hot swapping. There's another feature that's iffy, too, but I can't remember. It may be support for longer signal cable length. Without that the cable out to the external enclosure might be long enough to give some trouble, I don't really know.