Dell Command Update is not an Enterprise software tool and doesn't support the server platform. My expectation is that if you try to use Command Update, it will not work, because the associated repositories would not be accessible.  I would install OpenManage Server Administrator and check your firmware manually. The things to look at would be the BIOS, iDRAC, Lifecycle Controller, RAID controller, and NIC. You can compare them against the versions on the support site for the T310.   
l have an old Dell T310 Poweredge.  I would like verify my server has the latest updates of firmware, drivers, etc., and was wondering if it OK to use Dell Command Update to check for the latest updates?  
OK to use Dell Command Update with Poweredge Server?