Roku devices don't turn off, so yes, it's always drawing power, but it's minimal when it's idle (and pretty low when it's not). The power button on the remote is strictly for the TV. Depending on the Roku model there may be a "power saving" setting under Settings->System->Power. My testing shows this saves no more than a Watt or two and can cause more problems than it's worth.
The light should go off when either the screensaver activates or power saving mode kicks in, but it's become less and less reliable as an indication of anything with each Roku update. You'll find plenty of threads on the issue.
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