Yes, substantially — and the change is anisotropic, which is what makes it awkward.
Annealing means holding a printed part above its glass transition temperature so the polymer crystallises further. The part gains heat resistance and stiffness. It also contracts in X and Y and grows in Z, because the internal stresses frozen in during printing are released.
What that looks like in numbers
If a 50 mm dimension loses 2% during the cycle, it finishes at 49 mm. To end up at 50, you would have to model it at 51.0204 mm — a correction of 1.0204 mm.
A milder 1% contraction takes the same dimension to 49.5 mm and wants a model dimension of 50.5051 mm.
Those are large corrections by printing standards. PLA's ordinary print contraction across 100 mm is a few tenths of a millimetre; annealing can move a part by ten times that.
Why it varies so much
The amount depends on how much residual stress was in the part, which depends on print temperature, cooling, speed, infill and geometry. A dense, slowly-printed part relaxes less than a fast, sparse one.
That means there is no published figure to apply. The amount is a property of your print, not of the material, which is why the only reliable method is to anneal a test part of the same geometry and settings and measure it.
The distortion is not only linear
Parts sag. Held above glass transition, an unsupported overhang or a thin flat panel will deform under its own weight, and a tall part can lean.
The usual mitigations are to anneal parts buried in a bed of salt or sand, to support them on a flat plate, and to ramp the temperature up and down slowly rather than putting a cold part into a hot oven.
What you get for it
Meaningfully higher heat deflection and stiffness in PLA, which is the whole reason anyone does this. An annealed PLA part can survive temperatures that would sag an untreated one.
Whether that is worth the dimensional cost depends on the part. For a bracket, often yes. For anything that has to fit something else, printing it in PETG or ABS instead avoids the entire problem.
Compute a compensation for your own measured contraction in the shrinkage calculator, and see the process in the annealing guide.