A true oob port will have hardware and software changes that separate the traffic from the regular ports. However I have seen some oob ports that don't respect this and connect up the traffic as if they were regular ports. If you're expecting the oob port to not share the cpu and therefore be accessible during problems, then you're generally paying extra for that switch and not using a lower end model. You will simply have to test whatever brand/model you have to see it's behavior.
Of course you can use a regular port from the front of the switch as your oob management, but some companies can't afford losing even one port for this purpose. Most of the time the oob is abandoned and management is done inline across the trunk to a virtual interface. I mean if you have enough spare ports to use one exclusively for oob, then chances are you probably don't need oob at all and can just plug into the console port.
As for routing, in my experience, there is a special subnet used solely for oob and therefore routing is never needed. All the oob ports will be aggregated onto this subnet and a bastion host will be used to access anything on this subnet directly. So you don't need a "default" route, then you're sending traffic to a very small range of administrative hosts. A default route is meant to send traffic to the internet essentially, whereas your oob setup will have very specific and well defined hosts that will be accessing it. Therefore you can have a more specifically defined static route to send traffic out the oob.
The oob is not the same as a console port. Generally it's just a regular port in a physically different place on the switch and it's up to the software to keep the traffic separate. Again you get what you pay for and most of the time if the main switch is down, the oob is not much better. For the most part, the additional hassle of an oob setup is not worth it and the only time it made sense is when some manufacturing networks wanted total separation from the corporate networks. So you're not gaining much in terms of rescuing a down switch.