I do not wish to go down the road of installing the CiViCrm CRM but I do have a requirement to place REST calls to the API. Ideally I would like to do this (for simplicity) against the public accessible demo site. Can this be achieved? Presumably I would need need to generate an API Key?
This isn't possible, sorry. Could you say a bit more about what you're trying to achieve? I'm not sure how useful it is to do REST calls against a demo site.
While REST isn't available (the demo DB is reset daily, and the demo account does not have a publicly accessible API key), you can explore the CiviCRM API using the API explorer once logged in.