Is it possible to build a HA cluster with no shared network resource using only 2 or more servers?
as long as your have heartbeat between your ESX(i) Hosts, and can configure HA, this should work, but what is this exercise for? Also, if possible I'd prefer a 3 node cluster.
Do you have any description of such a solution, and maybe a video?
I'm not saying it will work as expected, I'm saying you could probably configure HA. As for your guests, they would/may fail over, but would receive no network connectivity.
I think best practice is always recomended, especially if you're looking to be supported.
A couple things I'll point you to.
http://www.yellow-bricks.com/vmware-high-availability-deepdiv/
http://www.vmware.com/files/pdf/techpaper/VMW-Whats-New-vSphere41-HA.pdf
even if you could configure it a failover would not happen as the datastore is unavailable on the other server. if you don't have shared storage you could look into using a Virtual Storage Appliance to turn your local storage into shared storage and do a failover that way.
Duncan (VCDX)
Available now on Amazon: vSphere 4.1 HA and DRS technical deepdive