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When I tried it the damage log showed it as being 13ms between damage instances from attacks while using W. Unless for some reason it doesn't play sounds, animations and show in the logs correctly. I did notice on hovering over damage that it does state that the attack time is 0.03, but it just doesn't seem like it.
Oh and i just tested, it does work. The max I was able to get for seconds/attack was 0.03s/attack, and the animation was fine too. Maybe you don't notice it because it's only for a short duration ( 3s only ) and it's really hard for the human eye to see difference between anything smaller than seconds you know lol. 0.03s - 0.13s. Just can't see the difference unless you watch it for a longer duration. Personally I feel his W is not worth it due to that short duration. Unless you get otherwordly core you can't be spamming that for it to be effective.
edit: after doing some testing it appears that 0.13 attacks per second is actually the limit, the animation and sound frequency goes up but dota doesnt actually apply an attack for some reason
So this means BAT is capped at some point or BAT doesn't affect the seconds per attack as aspd does or if that's wrong then seconds per attack is capped at 0.13 as lowest.
From what I gather the 0.13 seconds per attack limit is a hard engine cap, I'v tested it in IMBA with Night Stalker (who has no AS cap) and stacked thousands of AS, it would never go below 0.13.
This means even back then it never worked in reality. It just showed alch doing a sped up animation/sound but the attack rate was the same as when having a 0.13s/attack.
So i just read up on attack speed in dota. Apparently, seconds per attack is called Attack time which means time taken between attacks. It's different from attack rate or attacks per second.
Attack time = 1 / Attacks per second , So from this I am guessing attack rate or attacks per second is the limiting factor for this.