The big question is whether the mobo's BIOS supports booting from a drive attached to such a port. If it does, then Win 7 ought to be able to install on it and boot from it. Many eSATA and / or USB ports need drivers loaded from the boot disk before they can be used.
I'm intrigued that you say external drives are much cheaper. That is backwards from usual, but I know the market is odd currently because of the flooding problem in Thailand.
That board has a true eSATA port; running the machine from an eSATA drive on that port should be the same as running it with an internal drive.
But it seems kind of silly. It's a lot more vulnerable to spills and knocks that an internal drive. If you can REALLY get an external eSATA 2GB for less than an internal, just open it up, extract the drive, and install it internally.
But I agree with Paperdoc; that seems backwards, unless someone had a stock of crappy external drives around before the flood.