The recorded actions don't take wrapping mode into account; if they're an accurate reproduction of user input, logic follows that they'd behave properly with wrapping mode, as long as it is turned on when playing the action.
I figured there is some core component of the wrapping mode that's not implemented, since it doesn't support color picking either.

Reproducible: Always

Steps to Reproduce:
1. Make a new file
2. Turn wrap mode on (W)
3. Start recording
4. Make a stroke that extends past the edge of the document, looping around
5. Save recording
6. Undo all your changes or make a new project, turn wrap mode on
7. play your recording

Actual Results:  
The stroke doesn't loop around, it only extends to where it leaves the canvas.

Expected Results:  
I'd expect to get the same results as i get when i make the initial stroke.

This feature is pretty important for me.
It may be very niche, but i work with tiling textures that are a result of photogrammetry, and krita is the only tool so far that even remotely supports such a workflow.

I have a 3d scan of an object that i use to produce 2-4 texture maps (diffuse, height, normal, etc.), which i have to tile via recorded actions, so that the same operations (clone stamp, etc) are applied to all of them, producing minimal difference between the structurally identical texture maps.

Now, the recorded actions don't seem to support the seamless mode, which is one of the two possible tools to tile an image easily.
The other, less optimal solution would be offsetting by (width& height)/2, but the recording engine doesn't seem to record "Offset Image".