Not that I'm aware of. If you have some information regarding this connection to the 1st Tennessee Cavalry (US), I'd be very interested.

Here is a link to a site that includes a regimental history for this unit.

http://fifthtennessee.com/

And here is the Tennessee and the Civil War website history.

http://www.tngenweb.org/civilwar/usainf/usa5inf.html

Could you be thinking of the 5th Tennessee Mounted Infantry (US)?

Jim