Aside from lower market liquidity, would there be any technical limitations of an Augur fork built to run on Ethereum Classic? Could such an Ethereum Classic Augur fork that utilized Augur (Ethereum version) Oracles to settle its markets be essentially identical in both appearance, functionality and security?
There is no technical reason preventing Augur from being deployed on Ethereum Classic, or any other Ethereum network (e.g., any of the many testnets, a private network, etc.). You just need to upload the contracts and teach the UI of the address of the those uploaded contracts.
Augur is currently being beta tested on a couple different test networks, which goes to show that it isn't tightly coupled with the Foundation driven Ethereum chain.
While there is no technical reason preventing it from being deployed on ETC, I do not think it would necessarily be identical with regard to functionality or security.
Security wise, Ethereum Classic currently has less hash power than regular Ethereum. Additionally, once Ethereum switches to proof of stake, block times and transactions per second should be able to increase some. Proof of stake also enables sharding, which is widely considered not doable on proof of work networks. That said, these two features are probably at least a year away.