Does gigabit ethernet to thunderbolt adapter work with old ethernet?
From Thunderbolt to Gigabit Ethernet Adapter


  The Apple Thunderbolt to Gigabit Ethernet Adapter lets you easily connect to a high-performance Gigabit Ethernet network. Small and compact, it connects to the Thunderbolt port on your Mac computer and provides an RJ-45 port that supports 10/100/1000BASE-T networks.


So the answer is, yes it will work. It will provide the bandwidth up to the supported bandwidths 10/100/1000BASE-T as applicable.