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This is a networking question more than it is a ROS question. The answer is it depends on your computer's network configuration.

ROS publishes data to the whole of the network it's connected to, so if both of the ethernet ports on your computer connect to different parts of the same network then messages could be published over both ports. However if your computer is connected to two different networks then you control which one ROS connects to using the ROS_IP or ROS_HOSTNAME environment variables as described here.

Hope this helps.