If I spend 2 gold tokens in a turn with Sivir, Mercenary on the field, does that fulfil her condition to gain +2 might and ganking?

It depends on what you mean by "spend." Killing/using 2 Gold tokens just adds [A][A] to your Rune Pool — generating power isn't spending it, so on its own that does not turn on Sivir, Mercenary's +2 [M] and Ganking. (Same logic as FAQ #12831 for recycles.)

Her condition is "if you've spent at least [A][A] this turn." The bonus flips on the instant you actually pay that power toward a cost — a card's Power cost, an ability cost, etc. So if you use the 2 Gold tokens' power to pay [A][A] worth of costs this turn, yes, she immediately gets +2 [M] and Ganking for the turn (and it stays on even if the spell/ability is later countered). But activating them to float power in your pool isn't enough by itself.