It certainly was. And it was incorporated by the State legislature too, in March, 1860 as an association/regiment of volunteer militia...
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The 154th Tennessee Militia Regiment, volunteered as a unit into active service with the Provisional Army of Tennessee, May 14, 1861 for twelve months. It was tendered to the service of the CSA from August 13, 1861 as Confederate States troops, though retaining the name of their militia regiment until 1865.
The regiment was consolidated with the 13th Tennessee Volunteers in in 1863, forming thereafter the 13th & 154th Tennessee Volunteers (consolidated):
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These and other units were consolidated more fully in North Carolina in April, 1865 into the 2nd Tennessee Infantry (Consolidated)...
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Ultimately, it appears the name (numeral included) of any given regiment was immaterial to the armies. The Laws under which they were organized had perhaps more importance.
For example, some of the Militia Regiments that volunteered to serve as US troops. I recall the case of the 14th New York State Militia Regiment, which was designated the 84th New York Volunteer Infantry on mustering as three year troops, though they kept their State title so far as they could. I think the same with the 20th New York State Militia, which the USA recognized as the 80th New York Volunteers... I've seen where the Army didn't like them still employing their Militia regimental name, but the Governor approved, so the Army relented.
Some of the nine months militia regiments in US service in 1862-63, though technically militia, did not employ the term in their regimental name. For example the 12th-16th Regiments of "Vermont Volunteers." These regiments enumerated in continuation of the existing Volunteer Army regiments of their States... but as (volunteer) militia in US Service.
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Reading about these regiments, apparently they didn't want to be called militia, but "volunteers," as they were volunteer militia, rather than derived from drafts. The name meant little, as they served under the provisions of the July, 1862 militia act, and President Lincoln's calling forth of 300,000 militia in August, 1862 for nine months service, etc.