Certainly. That first ability is a trigger, that will go off when the Pyromancer enters the battlefield, so long after casting and even if it enters without having been cast. And it will trigger regardless of the number of cards in your hand. You have to discard two cards if you have them when that trigger resolves (or as many as you can if you have less than two), then you draw two cards, also regardless of how many you discarded if any. But for casting, the number of cards in your hand doesn't matter.
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Want to play a UW control deck in modern, but don't have jace or snaps?
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Former Rules Advisor
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(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
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Nexus MTG News // Nexus - Magic Art Gallery // MTG Dual Land Color Ratios Analyzer // MTG Card Drawing Odds Calculator
Want to play a UW control deck in modern, but don't have jace or snaps?
Please come visit us at the Emeria Titan control thread