It’s not about the capsules per se - nothing magical here; it’s the Movement Component - it only accounts for the root element of the actor, and here the capsule happens to be the root.
The Gun Capsule is ignored when the movement component calculates final movement position for the frame.
You’d need manually detect / track gun capsule and force the movement component to act accordingly.
Yet, one of the first disappointments the first time you make a game, adding collisions to the capsule does not affect the capsule. The capsule is a magic / special object that does not use the normal physics system.
(edit: I think you really meant: attaching collision components to the root component)
You do not add collision to the capsule - the capsule is the collision and it works fine with physics:
Irrelevant to the topic at hand but since it was mentioned - attaching collision to the root would work pretty well for physics sim. Welding kicks in and allows the root to take advantage of the attached elements’ collision - example.
attaching collision to the root would work pretty well for physics sim
The problem with this is that moving the character has little to do with physical simulation 
- so this does not apply.
From the component:
* Normally the root component of the owning actor is moved, however another component may be selected (see SetUpdatedComponent()).
* During swept (non-teleporting) movement only collision of UpdatedComponent is considered, attached components will teleport to the end location ignoring collision.
I’ve yet to play with this for anything serious but it might be worth looking into SetUpdatedComponent.