Yes, an NCO can command a unit in some situations, within certain limitations. AR 600-20 provides specific guidance on this issue. Review the following paragraphs:
2-8 Death, disability, retriement, reassignment, or absence of the commander reads in part:
Senior regularly assigned United States Army Soldier refers (in order of priority) to officers, WOs, cadets, NCOs, specialists, or privates present for duty unless they are ineligible under paragraphs 2–15 or 2–16. He or she assumes command until relieved by proper authority except as provided in c, below. Assumption of command under these conditions is announced per paragraph 2–5. However, the announcement will indicate assumption as acting commander unless designated as permanent by the proper authority. It is not necessary to rescind the announcement designating an acting commander to assume duties of the commander “during the temporary absence of the regularly assigned commander” if the announcement gives the time element involved. A rescinding announcement is required if the temporary assumption of command is for an indefinite period.
2-9 Absence or disability of all officers of a unit:
On death, disability, or absence of all officers of a unit normally commanded by an officer, the appropriate commander of the next higher command permanently assigns an officer to command, preferably of the branch to which the unit belongs. Pending assignment and arrival of the new commander, the senior warrant officer, cadet, NCO, specialist, or private regularly assigned to the unit will exercise temporary command. Restrictions on assuming command in paragraphs 2–15 and 2–16 apply. Assumption of command will be as noted in paragraph 2–8.
2-10 Emergency Command:
The senior officer, warrant officer, cadet, NCO, specialist, or private among troops at the scene of an emergency will assume temporary command and control of the Soldiers present. These provisions also apply to troops separated from their parent units under battlefield conditions. The senior person eligible for command, whether officer or enlisted,within a prisoner of war camp or among a group of prisoners of war, or a group of personnel detained by hostile forces or elements will assume command according to grade and date of rank seniority without regard to service.