In my Fallout Shelter games I normally keep the entry room unstaffed, and build no rooms on the first floor.
This means all Raiders, Ghouls and Death Claws go immediately to the 2nd floor, on which I have 2 full sized production rooms, stocked with my highest endurance dwellers equipped with my best weapons, and a Mr Handy on duty to help out.
My thought process is:
If I put a Mr Handy on the first floor, it will try to defend the entry room.
If it does this alone, it is doing damage to 1 invader, while absorbing all the damage.
If I put dwellers in the entrance, then I am doing 3x the damage, (and spreading the incoming damage out).
However, if I redirect the Invaders into a full sized room for their first encounter, then the Invaders are taking 7x the damage for the damage they are doing.
Of course, this logic only works if there is nothing special about combat in the entrance room specifically and/or external invaders are not scaled by room size or quality generally.
Best Answer
My answer would be "No."
A downside to defending the door room not mentioned so far is that the guys guarding the door aren't doing anything else. Whatever productivity you may gain from having raid/deathclaw events end a few seconds sooner will be massively offset (in my view) by having two high-spec dwellers spending most of their time kicking their heels in the entrance room instead of patrolling the wasteland or questing or crafting or producing stuff (or getting ).
If your vault is so well staffed that you can spare two people to do that, then go ahead, but otherwise it's a waste.