The remote object is available in all contexts. Now I am not certain about my context names but there is Share and Alfresco and remote is not available in Share (I think).
I do however know from experience where it is an isn't available and can describe the contexts
If you are creating a dashlet then in the dashlet javascript code that is run when the page is created the remote object is available. If you are ajax back to a webscript to get data from a dashlet once it has been displayed in a browser the remote object is not available, nor is it available in rules.
If anyone reading this can straighten me out my context names, I would appreciate it.