Never done it before and not sure if it possible, but I think to make it work you need to make a couple of changes.
So, lets assume that interface gi0/1 connects to Internet. This interface in your global routing table and g0 is in its own vrf. So, in order for gi0/1 to communicate with g0 you need to leak the global routing table to vrf Mgmt-intf (which defeats the purpose of putting management interface in its own vrf). Also if you are using private IP for your g0, and now you want to access it from outside you need to configure NAT. After all, I am not sure if it is good idea to expose the management port of you device to the Internet.
HTH