To be honest, I haven't used those REST calls, but I am pretty sure they will work on OnDemand, as the API is the same from the Server. There's no reason for them no to work.
My suggestion is for you to create a test OnDemand instance and give it a try, to make sure it fits your needs.
...It's true that there are projects in Jira; but they are merely a way to cut off issues, to tell them apart from other sections of work and to apply rules that are specific to that team (the schemes)....
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