No, this is not possible. There is no API to programatically set the user's alarm.
However, you can invoke the clock application to a specific view-state (alarm screen) and allow the user to set the alarm themselves.
Here's how to invoke an app: https://developer.blackberry.com/native/documentation/cascades/device_platform/invocation/sending_invocation.html
Here's the info on how to invoke the alarm clock: https://developer.blackberry.com/native/documentation/cascades/device_platform/invocation/clock.html