I'm wondering if we would have a category using the Companion App or if we would have a variable using the Companion app. That is if the Pip-Boy/Companion app would even be used in the speedrun.
Maybe, for dropping items for the hover glitch, equipping guns/items for killing enemies.
Maybe, but only as a variable. It's a pretty bullshit method that's only available to some, AND dependant on your internet connection, on top of that it doesn't change anything in the route unless glitches using it are found, so there is absolutely no reason to have a separate category for it.
I have used it and it could save a small chunk of time, you can manage inventory while walking, prepare FT while loading/talking ... It seems you can't spent perks point though.