You can expect sub-MOA, but don't think it's as precise as a supersonic bolt gun.
I threw together a Rem 700 .308 Win 16.5" bolt gun with a TBAC 30P-1.
I worked up a load using Nosler 140 RDF at 1050 fps, 34 ES, 13 SD that put 5 shots in 3/4 MOA on paper at 200 yards.
3 shots was down into the 1/2 MOA territory.
It's plenty good enough for hunting and plinking, but is not on the same level as supersonic loads in a bolt rifle.
With good equipment and components 1 MOA at 100 yards is reasonably easy to attain. 1/2 MOA is possible but a challenge. Precision and velocity down range does not degrade very much if you use a quality heavy match bullet (e.g. 200gr SIERRA matchking). These will maintain precision and velocity at 400+ yards but you basically have the trajectory of a mortar ... super fun.