Greek Gods are very very much deities Themselves. Binding yourself to a deity is not recommended if you don't have a close, personal relationship with the God/dess first.
For example, one of my Goddesses is Aphrodite (I'm a Hellene, so I just happen to work with Greek Gods and Titans). Though I follow Her and She guides me and has been for years now, I am not bound to her.
Why would you want to be bound to a deity? What's your reasoning?
The advantages would depend on the deity you are binding yourself to. I would recommend establishing a strong link with the deity beforehand and asking permission to bind yourself to them. It would most likely take energy from the deity, but with their level of energy, that shouldn't be an issue. If you have a spell to bind yourself to a deity, I'd like to see it so if you could send it to me in a message, it would be greatly appreciated.
I would not personally suggest binding yourself to a deity or any being. Even with people this can cause issues. If you wish to work on your bond, why not just use prayers and invocation, or dedicate yourself to them?
I've heard of experienced practitioners "horsing" and even godspousing. But bindings are meant to hold something, or two things together. I would think it offensive to try to force a god with binding. Not even sure if that would work, but my belief in gods is a bit different than most.