The solution you suggest is a viable one. You should be able to have access to the management interface of a device in this way. However, by doing so you negate the very purpose of an OOB management option. OOB is used so that in the event that a network goes down, you have an alternate path to reach a management interface without using the downed part of the network. With your solution here, you are depending on the production network to get to your management interface. It is essentially the same as obtaining management CLI access through a network SVI without the use of external cabling connecting particular ports to the management port.
Ideally, you should find a physically separate path to get to your management interfaces, and in some cases, this means the installation of new vertical cabling.
I hope this has been helpful!