I'm not sure if there's anything that will do exactly what you are looking for.
You could potentially group this stroked path with an object to allow it to be selected.
Or, you could rasterize the stroked path to select it.
Again, I'm not sure if either of those will work for you.
Maybe try enabling snapping and familiarizing yourself with the keyboard command for Outline Mode, Ctrl+Y or Cmd+Y, to help with selecting paths.
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