If I have a sprite token alone at a battlefield with a hidden smoke and mirrors and a unit in base can I react to the temporary trigger with smoke and mirrors to move my unit to the battlefield and hold?

Yes — that line works. The Sprite's Temporary trigger goes on the chain at the start of your Beginning Phase, which opens a chain and gives you priority. Hidden grants Smoke and Mirrors [Reaction], so you can play it from Hidden there: the first chosen unit must be the Sprite at the hidden battlefield, and the second (your base unit) can be picked freely because "another unit at a different location" is impossible to satisfy at the hidden battlefield (Rule 811.1.d.2.a). Since the Sprite has Temporary, the swap condition is met.

LIFO resolution: Smoke and Mirrors resolves first — your unit moves to the battlefield, the Sprite moves to base, and you draw 1 — then the Temporary trigger resolves and kills the Sprite at your base. Your unit is still standing there during the Scoring Step, so you hold and score the point (FAQ #12593, #5523).

Only caveat: the Sprite is what's satisfying the swap requirement, so if the battlefield were empty of your units when Smoke and Mirrors resolved, the swap would simply do nothing.