Depends on the wheel design.
You are correct, in most cases, if the offset is the same going to a smaller wheel will not make the brakes rub on the front of the caliper, but shrinking the wheel may allow the spokes to touch the top edge of the caliper, because the spokes do not go out as far on the smaller wheel.
So you may meed a larger spacer on a smaller wheel to push the wheel out further to get the spokes past the point where they touch the caliper.
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