if you can ping it, its a network issue. That means your management network has a route to the other ip. do a tracert and show that to your network guy. Also you only want to have one default gateway setup. BUT if you can ping it, it would be better to just use one NIC instead of two. its easier to manage and troubleshoot
No, its not a network issue, we have windows servers with the same configuration and you cant ping the external VLAN from the Management VLAN. It must be something with the CSA network configuration.