After I push a change to our assets origin, is there a way for me to check if this change has indeed cascaded everywhere on our CDN? I am looking at something similar to what OpenDNS Cache check does for DNS changes.
This is very much dependant on the CDN you use. As a basic guide the vast majority of CDN's only deploy content to the edge nodes when the content has been requested through that node. The best way to deal with this is to append versioning string to the end of your filenames such as
file.js?v=1.0.0 as a way to break both the browser cache as well as the CDN cache and fetch the latest version after a push.
Some CDN providers use a multicast network where you push content to one origin server and it is automatically distributed across the globe to all edge servers however this is not the vast majority of them.