Can I use Cisco Meraki, or similar, to deploy Mac App Store Apps? Cisco Meraki is fantastic, it blows the features of Apple's Profile Manager out of the water. One thing I would very much like to be able to do however is to push Volume Purchased Mac Apps to all our devices via Meraki, or something similar. 

Is this possible? We have iOS VPP set up perfectly to the point where apps can be one click installed - can this be done with OS X?
Yes you can. The process is the same as pushing VPP apps to an iOS device. You can look at this KB article from Meraki to see how it would work.