Let's say I have a Linux VM. Default route is the gateway to the top of rack switch for public internet and a public IP is bound on one virtual nic.
2nd interface is on a private network so the VM can be reached anywhere on the VPN. This is a management network where the gateway is on the other side of the data center.
A lot of stuff sits on the 10.0.0.0/8 that needs to reach this vm so a static route for the second interface points that /8 to that gateway on say 10.100.100.1
Now inside the same cabinet are devices sitting on 10.20.20.0/24.
If I didn't do anything, would hitting something on say 10.20.20.2 route traffic through gateway outside of the cab and back? I would think so as it sees the routing table and has no way of knowing.
If I want to optimize traffic so nothing is routed and traffic stays local to the cab, could I just add a third nic and give it an IP of say 10.20.20.3 and hitting .2 would arp / hit it directly through the switch in the cab?
It blindly follows the routing table from most specific and/or lower metric to the least specific/higher metric.
I don't fully follow your example (a diagram would really help here), but I think it would plainly not work. Packets needs to be able to flow both ways to work correctly (unless you're using a stateful firewall), so the source needs to be able to route all the way to the destination and the destination also needs to be able to send the response all the way back to the source. Both sides must agree on the routing.
ARP might save you there but there's still conditions where you might end up hitting the gateway for a local connection. It's kinda weird to have two overlapping subnets on the same local network, I would just avoid that.