I shoot muskets. I can tell you quite a bit about smoothbore muskets. I own one.
I don’t know if you can easily measure the MOA of a smoothbore musket. Smoothbore muskets fire round balls, and they pretty much always fire curve balls. The round ball will randomly contact the side of the barrel as it goes down, making it spin. The ball will go straight for maybe 50 to 75 yards or so, but after that, which way it goes is anyone’s guess. They used to say that you could stand 200 yards away from a single musketeer and not fear being shot by him (not entirely true, but you get the meaning).
You can make a smoothbore musket a bit more accurate by making the ball fit tighter in the barrel. Then it doesn’t rattle around so much as it goes down the barrel, though it still comes out spinning and thus will curve off randomly. But the tighter you make the ball fit, the harder the musket becomes to load after a few shots have fouled up the barrel with powder residue.
If you try to measure the MOA, you are going to get drastically different results depending on how far away you measure it, due to the musket ball’s spin and its resulting curve-ball nature.
With a pipe gun, since you aren’t muzzle loading it, you can make the round fit the barrel fairly tightly, which will help its accuracy. The round isn’t going to spin without rifling though, so any imperfection in the round will make it veer off course. An imperfect round from a rifle will spin due to the rifling, so any imperfection that makes it veer off course only causes it to corkscrew through the air - it still ends up close to its aim point. Even without imperfections, a conical round fired from a smooth bore is going to start tumbling at some point, which is going to make it veer off in some random direction.
A smooth bore musket is reasonably accurate to about 50 to 75 yards or so. Your typical smoothbore musket has a fairly long barrel though. The better fitting round of a pipe gun gives it an advantage, but the shorter barrel length gives it a disadvantage. I’d say it’s probably a wash, so accuracy-wise you are probably talking decent accuracy out to about 50 to 75 yards or so. Again, measuring MOA probably isn’t going to work very well since once the round starts tumbling its accuracy is going to go to hell in a handbasket right quick. A spinning round from a rifle will stay within a cone that you can measure. A round fired from a smoothbore weapon will have a trajectory more like a hockey stick shape - straight for a bit, then whizzing off in some random direction.
So a pipe gun is going to be horribly inaccurate compared to a modern rifle. But, most military engagements happen in the 50 to 150 yard range. A pipe gun will actually be ok on the short side of that range, though definitely not so good on the long side of it.
If the machine shop can rifle the inside of the pipe, the accuracy will increase rather dramatically.