Können is a model verb, which means it supports another verb. So you can use it like: Can-Eat, Can-Fly, Can-read, etc. If we were to use it for a normal sentence, we can say "I can eat" - Ich kann essen, and for a question "Can I eat" - Kann ich essen? The supported verb it always the full conjugated verb used for "Sie".
Your interpretation is close to what is meant.
"Can you hear me out?" or "Hear me out?" would be more asking the listener to allow one to finish rather than ending the conversation. It is a question requesting permission to finish rather than a statement telling the listener that you aren't finished yet.