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Unfortunately, that kind of thing is not possible with a Hatch pattern. You could get close with a series of Offset Arcs, using a Linetype that incorporates a brick Shape, similar to this:
That was built to do brick edges, along non-curving-brick-field hatching for a brick pathway, or a concrete sidewalk, so its Shapes have their long direction perpendicular to the Arc "path," but it would be easy to make a variation with them parallel to it. If I post the Shape and Linetype files behind that, are you capable of adjusting them?
The difficulty is that this won't really "do what you want" where Arcs using such a Linetype meet edges of the area, openings, etc. You would need to do a lot of tweaking of the length and end positions of the Arcs, and fill in the partial-brick perimeter conditions, which may be as tedious a process as Arraying brick-shaped Blocks or rectangles and Exploding and Trimming and so on.