The battle of Pea Ridge was fought on March 7-8, 1862. Brig Gen Albert Pike was in command of all Indian troops of the Indian Territory. Pike had negotiated all the treaties between the tribes of the Indian Territory and the Confederacy. Acting Brig Gen Colonel D.H. Cooper was his subordinate.
O.G. Welch's Squadron of Texans was part of the 1st Choctaw & Chickasaw Mtd Rifles regiment and they did accompany Pike to the battle. The balance of the regiment lagged behind and never reached the battlefield, stopping at Camp Stevens where Pike found them on March 8th.
Below is an excerpt of Pike's report of the advance and retreat from the battle. The report in its entirety can be found in the "Official Records" which can be found online at Cornell University's 'Making of America' site at http://cdl.library.cornell.edu/moa/browse.monographs/waro.html
The War of the Rebellion: A compilation of the official records of the Union and Confederate armies. / Series 1 - Volume 8, Page 286
DWIGHT MISSION, CHEROKEE NATION, IND. T.,
March 14, 1862.
SIR: On February 25 I reached Cantonment Davis, near Fort Gibson, with Colonel Cooper's Choctaw and Chickasaw battalion, which had been encamped near the mouth of the Canadian. The same evening Colonel D. N. McIntosh's regiment of Creeks arrived at the same point. I had in charge a large amount of coin and other moneys for the different Indian tribes, and found delegations of the Osages, Comanches, and Reserve Indians awaiting me, and the disposition of the moneys left unexpectedly in my hands, together with the delights with the Indian tribes, detailed me there three days.
The Choctaws, Chickasaws, and Creeks refused to march until they were paid off, and as by their treaties with us they could not be taken out of the Indian country without their consent, I had no alternative but to submit. The payment of the Choctaws and Chickasaws occupied three days.
On the morning of the third day I left them behind at Fort Gibson, except O. G. Welch's squadron of Texans, part of the First Choctaw and Chickasaw Regiment, with which, and the Creek regiment, whom I persuaded to move by the promise that they should be paid at the Illinois River, I marched to Park Hill, near that river, remained there one day, and not being overtaken, as I expected to be, by the Choctaw and Chickasaw troops, moved the next day, Monday, March 3, towards Evansville, and the next day to Cincinnati, on the Cherokee line, where I overtook Colonel Stand Watie's regiment of Cherokees.
...
General Cooper, with his regiment and battalion of Choctaws and Chickasaws, and Colonel McIntosh, with 200 men of his regiment of Creeks, came up with our retreating train at Camp Stephens, where they found Colonel Drew's regiment, and remained with General Green, protecting the train until it reached Elm Springs, where they were all ordered to march with their own train to Cincinnati.
The Choctaw and Watie's Cherokee regiment seemed ready to fight outside the Indian Territory when they had sufficient ammunition, food, etc. to do so. They used their right of refusal to negotiate -- in this case to get their past due pay. They did not venture far from the border of the Indian Territory, e.g., Newtonia MO, Jenkin's Ferry AR, but they were willing to operate outside their borders.