There's no big advantage to installing the "fat tube" early in the process. As mentioned, it will scrape the primer or paint off if left hanging on one end, or will be in the way of other work. While you'll need to drill it to the elevator horns at some point, they will likely go in and out several times during the build. Fitting and sanding the elevator tips comes to mind.
That back pushrod is a bugger to connect properly with all the spacers and washers that are required. You can drop a bolt through there just to hold it all together in the meanwhile, but the final rigging will require that the stick grips, instrument panel with switches, and several other components be in place to ensure proper range of travel.