How to run automated GUI tests on a remote headless ESXi Virtual Machine?

Question

I'm trying to setup automated GUI tests in ESXi Virtual Machines using TestComplete. The problem, as I understand it, is that when no remote desktop connection is made to the ESXi virtual machine, then it is impossible for TestComplete to perform screen captures and therefore automate the GUI testing. As far as I understand it, this is due to the fact that Windows does not generate any user interface when nobody is viewing it.

I'm sure other have experienced this problem. How did you solve it ? Are you using a third party computer which automatically launch remote desktop connections prior to running the tests ?

Would it be possible to launch a remote desktop from a head-less virtual machine to another to fake somebody viewing ?

Any other smarter solutions I haven't thought about ?