It's possible that Private Varnum was wounded at Tazwell, Tenn. on August 6, subsequently treated in a hospital at Bean's Station where he died September 4, 1862.

The Forty-sixth was organized at Loachapoka, in the spring of 1862. Shortly after, it was sent to east Tennessee, and had several casualties in the fight at Tazewell. The regiment was in the weary march into Kentucky, in Stevenson's division, but did no fighting.
http://www.archives.state.al.us/referenc/alamilor/46thinf.html

Here are notes of the 31st Tennessee Infantry, a sister brigade under the command of Col. A. W. Reynolds, Stevenson's division. I would assume that the 46th Alabama in Taylor's brigade followed a similar path.

JOURNAL OF J.M. BIGGS
31ST/39TH TENNESSEE MOUNTED INFANTRY

Saturday July 5th, 1862, Rutledge, TN:
June 11, the regiment returned to Knoxville from thence to Clinton, thence towards Cumberland Gap. I took the mumps on the road between Clinton & Priceville, June 13. Left the regiment Sunday, June 15 and went back to Knoxville from there June 17 to Greene County, staid in Greene County till July 3, from there to the regiment where I arrived Friday, July 4th. Encamped at the Medical Springs near Rutledge, Grainger County, Tennessee.

July 11, 1862, near Blaine X Roads:
Took up line of march Sunday July 6th, from 4th Brigade (Barton’s) to 5th Brigade (Taylor’s) and arrived at Cedar Ford July 8th. July 9th we left Cedar Ford and came to this place of pines and chiggers and I’ve a few less than ten thousand on one.

Friday, August 1st, 1862, Camp Elzey near Blaine’s X Roads:
July Sunday the 20th, the regiment marched about 7 miles towards Mainardsville & camped in an apple orchard. At 1 o’clock, Monday morning, took up the line of march for Powder Spring Gap where we remained till Sunday, July 27th. From there crossed to the south side of Clinch Mountain. At 3 o’clock, Monday morning marched towards Rutledge, went within 2 miles, rested a few hours then back to the same place where we started in the morning. Tuesday morning at 3 o’clock started for this place & got here in time for breakfast.

August 21, 1862, near Tazewell:
The regiment left Blaine’s X Roads, August Fourth and marched above Mainardsville within about a mile of Clinch River, distance some sixteen miles. August 5th moved up the valley to the fork of the Tazewell & Big Spring Roads, about ten miles. August the 6th, our forces marched from the forks of the road to attack the enemy at Tazewell. The engagement commenced about nine o’clock in the morning by the enemy shelling our pickets. They were charged by the 3rd Tennessee & put to flight & retreated in disorder some two miles. The 3rd Tennessee lost forty men in killed and wounded. Saturday the 16th, our forces moved towards the Gap & arrived there Sunday, distance 12 miles from Tazewell.

October 4, 1862, Camp Breckinridge, Garrard County, KY:
September 17, the Yankees evacuated Cumberland Gap & on the 18th Col. Taylor’s Brigade took possession of the place.