It does not.

Nor could I find him in Shaler's Infantry regiment [27th Ark] or Harrell's Cavalry Bn. Many of the men from Adams' regiment were distributed to these two units.

From The Alexander Papers, we learn of the final days of the existence of this regiment:

Battle of Prairie Grove-Hindman's report regarding Adams’ regiment noted, the field and staff officers who had been appointed rallied about 75 men of the Regt around the colors, and these did much to redeem the reputation of the regiment. With but few exceptions, the company officers exerted no influence.

12/16 -camp near Van Buren
VII. Adams regt of Ark Infy of Shaver’s brigade having been so reduced by desertion as to be too weak for service as a regt men to be distributed among co’s of Shaler’s Ark regt of same brigade officers of regt to report to hdqrs after the distribution above directed shall have been affected.
Gen Frost cdg 3rd Division will cause this order executed at once

12/16 HQs Adams’ Regt To Col Shaver, Cdg Bgde-To you, and through you to the Major-Gen cdg Corps, I respectfully present the name of John Howerton, 3rd Corp of Co “A” of my Regt, as the soldier entitled by meritorious conduct to the gun proposed to be presented by the Maj Gen cdg Corps.
Corp Howerton was one of my Color Guard on the day of the battle of Prairie Grove. The Color Sgt being sick, Howerton was designated by myself to bear the colors of the Regt. As stated in my report, my Regt went forward under a brisk, I may say heavy fire of Arty and small arms, and remained under a terrific fire for more than half an hour. Of the eight corporals composing my Color Guard, five were killed and two wounded. My flag is pierced by nine balls, yet Howerton never in the least degree faltered, never but when ordered by myself let the flag drop in the least, and in the confusion which ensued in my Regt when repulsed in the first charge, and when Major Williams and myself were using our utmost exertions to rally the men under a heavy fire, Howerton steadily upheld the flag and used both word and action to prevail upon the men to rally to their flag. His entire conduct on the field gave the fullest evidence of cool, unflinching courage and bravery. He bore the flag safely from the field, and I can but think that if true bravery is to be rewarded by so beautiful a present as the gun in question, Howerton’s cool bravery under most trying circumstances entitles him to the handsome reward.
I have the honor, Sir, to be, Your Very Obt. Svt., Chas W Adams-Col Cdg Regt.
[Endorsements]
Hd. Qrs. 2d Brig. &c, Camp Mazzard, Dec. 18, 1862.
Respectfully forwarded for consideration of the Brig Gen Cdg Div-In my opinion the gallantry of this Color Corporal deserves to be rewarded.
R. G. Shaver, Col Comdg.
Hd. Qrs. 3d Div., Dec. 18/62- Recommendation of Col Shaver fully concurred in-Von Puhl for Gen Frost

12/18 Spec Order 68
III. Col Charles W. Adams and Lt. Col James Fitzwilliam, of Adams Regt Ark Infantry, are relieved of duty, for the time being, with their regt, and will report to these Head Quarters for special instructions.
IV. Maj. J. K. Williams of Adams regt Ark Infantry is assigned to the duty of collecting in camp of instruction at Clinton, Van Buren Co, Ark, or such other points as he may find eligible for the purpose the men of that regt who have deserted or absented themselves without leave. He is authorized to give to such men the particular announcement that all who report to him for duty by or before the first day of February 1863 and remain in camp faithful soldiers will be pardoned all past offences. Those who remain out beyond that time or whom it may be made to take by force will be dealt with as their conduct deserves. The several Capts and Lieuts of the various companies will report to Maj. Williams for duty, and obey his orders. The Adjutant, Surgeon, QM and Commissary of the regt are likewise placed under his orders. He will from time to time report to these Head Quarters giving detailed information as to his progress in carrying out these instructions. Should he find it practicable to enlist men not now in service he will apply specially for authority to do so.

1/30/63 to Holmes-regarding Adams’ Regt- men to be assigned to Shaler’s Ark Regt per spec order 28 of Jan. 29-
Hindman also says Col C W Adams is now indispensable on my staff and wishes to keep him...................
He is the best I have seen in the war as AAG
Officers of Adams Regt to be mustered out-most of them are at Clinton trying to gather and recruit their Regt-any thereby gathered to be turned over to Shaver since that is in his recruiting district.