Does ServiceStack offer out of the box support for verification of email addresses and phone numbers (via SMS)?
No we don't include any higher-app-level functionality with infrastructure dependencies like Email or SMS gateways in our core packages. You can find what features we have listed in our documentation website: http://docs.servicestack.net
All that's built in is Fluent Validation's EmailValidator.
You can submit any feature requests them to https://servicestack.uservoice.com