No, users are required first invoke the skill with their voice to get a response. We're working on push notifications, which will be available soon, which may do what you want: https://developer.amazon.com/blogs/alexa/post/8cc45487-d5fb-413b-b6c7-eeea4794d10c/amazon-announces-notifications-for-alexa-feature-is-coming-soon-sign-up-to-stay-tuned.
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