Well, nothing out of the box (at least in the C# client) supports it. You might be able to leverage the console plugin with the vSphere web client... I'm less familiar with that, so I won't say 100% no. I don't usually answer threads with "no" unless I'm pretty certain, but I would love to be wrong here!
If you're desperate, you can whip something up to pull screenshots using the vSphere web API. Kludgy, but it's worth mentioning. 
http://www.doublecloud.org/2010/09/really-easy-ways-to-capture-vm-screenshot/
Hope that helps!