Question about Hecarim's E

Okay so I consider(ed) myself a hecarim main and now I think I'm learning something new.

I've been playing a lot with my friend who is still leveling his account and he asked me when playing hecarim:

"Should I use E before I ult because I travel further"

At first I was confused because I always use E before ult when I'm engaging (it's already powered up so I can displace an enemy after ulting while dealing reasonable damage). But he said I didn't really answer his question and that he was talking about the bonus damage from "traveling"

This is how I always understood Hecarim's E:

• Devastating charge has 3 stages of movement speed
• The last stage gives the most movement speed
• The movement speed is converted to ad from your passive, therefore making it so your devastating charge "charges up" power so you would deal more damage after building up more movement speed.

But after what my friend said and after reading the abilities description again I'm wondering if I'm understanding this correctly: -Devastating charge's deals more damage the further you travel -It also increases your AD because it increases your movespeed

If so then that really explains all of my unanswered questions about how hecarim's optimal homeguard-tp-gank worked (but early homeguards were removed anyways and so were homeguard tp ganks)

Edit: He also asked me if he used E before going through an ally (presumably max level) bard tunnel would it count as distance traveled and increase the damage (If the above statement is true)?