Artificer would struggle to replace the Wizard. You might be able to pull it off, but it wouldn't be a clean fit.
Artificer probably cannot replace a Fighter, even with the appropriate subclass. I could see them being a decent "off-Fighter" if we wish to view it that way.
That leaves Healer and Lurker/Skillmonkey. The spell list makes healing doable, but not nearly at the level of a Cleric....but subclasses fill that hole. So yes, an Artificer can replace a Cleric, I'd say, based on their spell list. I can also see an Artificer that replaces a Rogue, and is focused on utility effects and spells, scouting, stealth, etc. The Armorer subclass can fill parts of the Fighter role, namely the defensive parts, to some degree. In 4e terms, the Artificer can "flex" into a defensive direction, but will have to do a lot of the heavy lifting themselves (or from other sources, e.g. physiological features, background, equipment, etc.)
So...yeah. Artificer fits into Cleric and/or Rogue space. It has certain similarities to Bard.
Also, just to point out...these are extremely close to the roles of 4e. Bard and Ranger are the only two classes listed which appear on multiple lists. 4e Bard could MC into any other class--thus giving it amazing flexibility for building into any role the player wanted. Rangers were surprisingly hardy for a Striker...and did do skill-y things in addition to fight-y things.
Just find it so funny that people rail and rail and rail against roles....and then everyone goes back to agreeing that roles do in fact exist in practice, that the game is in fact designed with such thoughts and expectations, and that despite this fact, people have always been able to play what they want and not give a damn about it. It's just bitterly hilarious that we all TALK about classes as having roles....but having the books in any way recognize that they have roles? You've just destroyed everything good and right and true! How dare you! Nerf darts at dawn!!!