In that case, yes a banana and a glass of milk sounds like it's better than not eating, especially if you know that it makes you feel a bit better in the morning. And if you will eat it, it will give you at least something to start the day.
If you wanted to push it, you could blend it and put a dollop of peanut butter or natural yoghurt and that would increase the protein and calories and it's easy to drink if you prefer drinking to eating first thing.