The answer is: there is no clear answer for all boards. There are some features in eSATA that are optional and MAY be included in a regular SATA controller, or may not. It depends on what the controller manufacturer decided to do. The two most important items like this are support for hot swapping, and support for longer eSATA data cables to allow for reaching an external device.
You can try using the cheap adapter that converts an internal sATA port to one that is easy to access on the back plate, although this does not make it an eSATA port. Then see how it works. If it works reliably, the cable length issue is a non-issue. If you do not need hot swapping, that also is a non-issue. Or, if you need it and it works, maybe the controller maker built that feature into their standard SATA controller. Worst case is it does not work and you have wasted $10 on an adapter when you now need to buy a proper eSATA controller. If the adapter came free with the external case, then you've only wasted time trying it out.