Q:

Encrypting all internal communication on an ESXi box

Lets say I have a large system made up of many VMs running on one bare metal esxi box.  Each of these VMs are running application(s) that are necessary for the system.  I do not have the ability to change some of the applications, and changing the others would be difficult.  Many of these applications send passwords around in clear text, you know, like you do.  
I would like to explore a system wide solution. Can an ESXi hypervisor be configured so that all "virtual" ip traffic between these virtual machines is encrypted?  
I don't mean changing the VM Guest operating systems to use ssl or anything like that (if possible to avoid). Rather I want ESXi to handle encrypting and decrypting data between these virtual NICs; or any other solution that sufficiently hide this data.

A:

Can an ESXi hypervisor be configured so that all "virtual" ip traffic
  between these virtual machines is encrypted?

No, but it's a switch not a hub, not on its own anyway - you could, if you really wanted to be paranoid, use NSX which provides microsegmentation between VMs but that's not encrypted, just firewalling.

