Can a Commander-in-Chief serve in the military (in Guard or Reserve Status) at the same time?
More info:
https://www.trumanlibrary.org/lifetimes/military.htm
http://www.trumanlibrary.org/hstpaper/rg407.htm
I see he was Retired from duty prior to becoming CoC.
But he was a Senator and attended at his own expense, how many of us would do that today!
I love this part of the link...
Forging Ties in the Reserves
Truman's military ties during World War I continued long after his experiences on the battlefields of France. Following his discharge in 1919, he missed army life and decided to return to Federal Service through the Officers' Reserve Corps. Although Colonel Truman completed his final stint of active duty in 1933, he was appointed commanding officer of the 379th Field Artillery and attended unit training during the summers of 1936 through 1938 at his own expense. Truman's own military service formed his views on security and defense. He became a strong advocate of military preparedness as the best method to deter future conflicts.

Truman Library - Records of the Adjutant Generals Office: Military Personnel File of Harry S....
Size: Less than one linear foot. Access: Open. Copyright: Documents created by United States Government employees in the course of their official duties are in the public domain. Copyright interests in documents that do not fall into this category are presumed to remain with the authors of the documents or their heirs. Processed by: C.W. Orhvall (1977). Updated by: David Kreidler (2005) as part of the Truman Library Internship Supervising...
The Pulitzer Prize–winning biography of Harry S. Truman, whose presidency included momentous events from the atomic bombing of Japan to the outbreak of the Cold War and the Korean War, told by America’s beloved and distinguished historian.The life of Harry S. Truman is one of the greatest of American stories, filled with vivid characters—Roosevelt, Churchill, Stalin, Eleanor Roosevelt, Bess Wallace Truman, George Marshall, Joe McCarthy, and...

Military members serving in active political positions? | RallyPoint
We all should know that service members cannot express political opinion in uniform, or as a representative of the US Armed Forces. However, there are many examples in history when members of the Armed Forces were not only politically active, but were even serving in full time political jobs. For example, take former Senator Scott Brown, who served as Senator of Massachusetts while simultaneously serving as a Lieutenant Colonel in the MA...
That said, it would practically be a horrible, very bad, not good idea. First, there is an inherent conflict of interest (if nothing else, presidents approve promotion lists...). Second, there is the chain of command issue (as others have pointed out, bossing around the President, or issuing him a bad OER is probably going to end poorly...). Third, the job of President is more important than anything else this person can be doing with their time. If the President is spending enough time to maintain his military proficiency, what is not being done in its place? All of the above could be logically extended to anyone in elective office (and I do!), but with the President, it steps up several levels of magnitude.