Looking at the online Missouri Secretary of State's website for Missouri State Archive military service records I found four possible George Allens who may or may not be the man your seek. Bear in mind that the military often mangled spellings and was bad about getting the middle initial wrong with names, too. I found none listed for the MSM and these four in the EMM or Provisional EMM:
--G. J. Allen was 5th sergeant of Captain Denny's Company H of the 46th EMM serving out of Roanoke, at the intersection of Howard, Chariton, and Randolph Counties. This Allen's record only mentions him at the outset of the EMM program in early September 1862 with no notation of any active duty.
--George H. Allen was sergeant in Captain G. W. Cunningham's Company A, 35th EMM serving out of Brunswick in southwest Chariton County. This Allen's record says he performed 272 days of active duty between 26 July 1862 and 30 April 1863.
--George W. Allen was private in Company I of the 2nd Provisional EMM serving out of Milan in Sullivan County. This Allen's record says he served on active duty with the 2nd PEMM between 21 March and 1 October 1863 (probably let go when the General Assembly and the EMM apparatus stopped the PEMM program in October 1863). This record says that Private Allen was detailed into the 2nd PEMM from the 66th EMM, but there is no record card for Allen's service in the 66th EMM. After being discharged from the 2nd PEMM Private Allen would have reverted to the 66th EMM.
--George W. Allen was private in Captain Dubach's Company E, 53rd EMM serving out of Hannibal in southeast Marion County. This Allen's record says he performed 193 days active duty between 1 September 1862 (about the beginning of the EMM program) and 12 March 1863, and that he was present at muster calls on 30 April, 30 June, and 20 August 1864, too.
That's all I could find online unless the EMM spelled your Allen's last name another way.