Well, if we look at it from a design viewpoint, it's supposed to be one of his "Escape" abilities that the "Assassin" side of him is intended to have.
Looking at our wondrous LOL Wiki,
falls under both the Slayer (Assassin Sub-Class) and Controller (Catcher Subclass) roles.
Slayers (Or more specifically, the Assassin Subclass) has this in their description. (Now this is written by anonymous contributors to the Wiki, not Riot employees themselves): "Due to their mostly melee nature, Assassins must put them themselves into dangerous positions in order to execute their targets. Luckily, they often have defensive tricks up their sleeves that, if used cleverly, allow them to effectively avoid incoming damage."
So looking at it that way, the ability to vanish and then proc his passive's heal makes sense.
But I can also see where you're coming from on this, as in the (presumably) hypothetical example you gave of him being under the effects of a DoT such as
, or any other DoT effects (Like Singed or Teemo's poison, or Nautilus' W DoT, or Darius' bleed as additional examples) should technically render him incapable of doing something like this:
: And for my next trick, I will turn... INVISIBLE! Activates W POOF! I'm gone!
: OK, wait. He was just bleeding profusely because I had my Noxian Might on him. The F*ck'd he go?
But he's also a "Support" under the Catcher Sub-Class. It says the following about them: "Although not as reliant on their friends as Enchanters, the fragile and immobile Catchers greatly benefit from allied presence - both to deter incoming danger and to help capitalize on targets they've locked down."
(These are not the ENTIRE transcripts of the descriptions, just as a heads-up)
So that makes it something of a contradiction. He's not intended to have escapes (As a support, one is supposed to be reliant on one's allies), yet he does.
In HotS (Heroes of the Storm, I play that along with this) some of their "Assassin" characters can also turn invisible (Such as Nova, Zeratul, Valeera). Some can even render themselves Un-revealable, if they take certain talents in their talent trees. I think that's something Riot applied to Pyke here with his W. A sense of that same "Unrevealable" nature, if you will.
I guess what I'm trying to say is, I don't fully agree with it either. But, while that "Assassin" part of his kit does seem odd, it's off-set (For the most part) by the fact that he has the fragility of the Support/Controller that he is and is very "feast-or-famine" (From what I'VE experienced). If he (And by extension, his ADC) can't get fed, then this "bonus" provided by his W can be considered acceptable to try and break him out of slumps. But that depends on skillful use/play by the Pyke themselves.