Can I Use A Usb To Ethernet Adapter To Network An External Hard Drive

Basically, my question is, will the router recognize it and know what to do, or do I need special software and if so where would I find it? If the adapter I showed above won’t do the job, is there one that will?

Other random info: all computers in the house are Windows (XP - 7).

If you need to know anything else let me know.

Thanks,

Izzy