I'm not faimiliar with STAF/STAX, but you can try to install it but I'm guessing you tried and hit some type of roadblock. ESXi runs a limited Busybox console which has a limited set of tools/libraries, so if STAF/STAX has depednencies that just are not available, then you won't get far.
Having said that, the recommendation is to see if you can build a statically linked binary of STAF/STAX to "potentially" run on ESXi, this as you know is not supported but here are a few blog posts that may help you investigate this:
http://www.virtuallyghetto.com/2011/02/how-to-compile-statically-linked-rsync.html
http://www.virtuallyghetto.com/2011/02/how-to-compile-busybox-for-esxi-kind-of.html
http://www.virtuallyghetto.com/2011/02/how-to-compile-busybox-for-esxi-kind-of_15.html
If you really need to support this, a better recommendation is if you can get in touch with VMware through their partner program, if you are developing a product/etc. they can help you with this type of request and even provide you with a way to accomplish this. Basically if you can get an "application" running in version of Busybox that VMware uses, then it should work but again you'll need to work with VMware for the technical details as its probably not a standard Busybox distro as they have modification to the source code
Good Luck
