Even if a live support is with you all the time they would also tell you to wait because most support doesn't have the same powers as an admin. .
You already have the mods in the chat, don't they provide enough relief if you're looking for a person who could assist you? I agree with Avirunes that it's unnecesary to have a support.
Having a dedicated chat support is not a bad idea as majority of the professional gambling sites will implement these to facilitate proper support round the clock and no admin will share the back end privilege to mods in chat but the admin can share the necessary privilege needed to sort basic customer issue if there is a dedicated chat system and it will be a great addition to any platform and it will attract more customers.