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This is a serious limitation. There are HUGE amount of possible skills implementations where pressing the button could have Alexa start talking. Lot of people are reluctant to start talking to Alexa in public places, and may feel silly, but being able to press button and have Alexa start engagement would open gadget usage to wider audience. Using it only to build some silly games it's a waste of time IMO.
No, a Skill can integrate Echo Buttons using the Gadget Skill API, but pressing an Echo Button outside a Skill session won't trigger events to a Skill.
Sounds a really cool idea, submit a feature request so we can route it to the Gadgets Team.
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