Does an instant that is exiled with {elite Arcanist} benefit from {goblin electromancer}? Likewise {guttersnipe}?
You can't cast instants with x in the casting cost from elite arcanist right?
Alrighty. So, when you activate the Arcanist's ability, you look at the converted mana cost of the exiled card. You pay what's written on the card, copy the card, then cast it without paying its mana cost. Since Electromancer only applies when you're casting the card itself as a spell, you don't get the bonus here (since you're casting it without paying the cost). To answer the X question - You can, but X will always be 0, since when you cast a spell without paying the cost, X is always 0. Likewise, when calculating the mana cost for paying for Arcanist, you leave X at 0.
Since the ability still instructs you to CAST the spell, it will trigger things like Guttersnipe, though.