Yes. When you remove the last suspend counter, you cast the spell from exile. This will trigger any abilities that trigger off of spells becoming cast. Vial's ability doesn't care how or where the spell is cast, just that it was.
November 16, 2016 11:24 p.m.
Important to remember is that the converted mana cost of a card is based on the mana cost written on the card, not the mana spent to cast it. Casting Rift Bolt off suspend would cause 3 damage and Wheel of Fate would cause 0 damage. Also, casting off suspend will likely be the first spell you cast on the turn, so subsequent spells on your main phase won't trigger Vial Smasher. Conflagrate will see in the mana cost even if you're paying X by discarding cards, and Bonfire of the Damned will see both X's even if you're paying the miracle cost.
November 17, 2016 7:37 a.m.
Now that Neotrup went into X spells, I think it should be explicitly stated that while Vial Smasher's ability resolves, X has a value, meaning a Bonfire of the Damned cast with Miracle for will have a converted mana cost of 15 (7+7+1) and Vial Smasher will deal 15 damage, followed by Bonfire of the Damned dealing 7. While quite obvious, note that you won't know which opponent Vial Smasher will deal damage to when you have to choose a target for Bonfire.
For completeness' sake, let's also add that Suspend is a special action that doesn't use the stack and is not a spell, so suspending a card won't trigger Vial Smasher - only casting the card when the last time counter is removed does.
November 17, 2016 10:49 a.m.
That is, the act of suspending doesn't use the stack. Removing a counter does use the stack (but doesn't trigger Vial Smasher), and casting from exile of course both uses the stack and triggers Vial Smasher.