Yes, I believe there was a workhouse in County Monaghan, only because each Poor Union was required to build one. I believe a George Harrison was elected to the relief committee and it was the committee's job to oversee the workhouse. At first it was an elected postion, and the next two times the law changed it was an appointed position.
I doubt your Duffys were in the workhouse because I associate the name Duffy in County Monaghan with that of the revolutionary or the one who was with Young Ireland. Often those who were politically active were not destitute, but better off, able to eat, able to perhaps afford a gun, literate or educated, middle class, sons of larger not small farmers. If better off, then your family might have been "rate payers" who were paying for the workhouses, the road building projects, the soup kitchen. I am rereading Cecil Woodham-Smith, The Great Hunger Ireland 1845-1849. There are a couple of references to Monaghan, and there was great hunger in Monaghan.
As far as I can tell 1/3 of Ireland was regularly hungry, and those people during the Great Hunger were definitely bad enough off to need free food. How many additional people in County Monaghan bought corn meal at the market rate or were given work or free soup I do not know. Also 1/3 of the estimated 9,000,000 Irish died or immigrated due to the Great Hunger. It is hard to tell what one's ancestors were doing at this time. I hope that someone else who knows this time period better than I do will reply. Hope this helps.