At the moment the vision is to avoid them going into Gmail, or other email clients/services at all, other than sending an email notifying you of a new inquiry...
We believe that managing them in Gmail is ok, but we've found it to be less than reliable, it's easy to un-star an important email and forget it never existed, or indeed miss an inquiry due to spam filters etc...
However i'd be interested in hearing why Gmail integration would be good for you?