I've just purchased the E1200 Pro tuned upgrade for the S900. I thought that before installing the arms on the S900, I'd connect them up to the ESC Updater to configure the LED colour and check whether there are any firmware updates.

I connected the JST cable to the USB tool and run the ESC Updater app (Mac). However, I get a solid green light in the app, but it doesn't connect to the ARM The blue light in the app remains dimmed. Does the arm need to be connected to the S900 before it will work? If so, does the S900 need to be powered up?

yes it needs  to be connected