Can you react with Ambush in your beginning phase to a temporary unit on your battlefield dying? Do I get the hold effect and points if I do so? (I.e. I had a single temporary sprite on the battlefield)

Yes, you can react to your "Temporary" unit's death trigger by playing a unit with Ambush during your Beginning Phase, and you will maintain battlefield control to score the Hold point.

Sequence of Events

1. Beginning Phase Trigger: At the start of your Beginning Phase, the "Temporary" keyword triggers because your unit is slated to die. This trigger is placed on the chain, creating a [REACTION] window.
2. Reaction: You play your unit with Ambush as a [REACTION] to that trigger.
   • Note: According to Rule 822.1.b, Ambush allows you to play a unit as a [REACTION] to a battlefield where you control units.
3. Resolution (LIFO):
   • The Ambush unit resolves first, entering the battlefield.
   • The "Temporary" trigger resolves second, causing your original Sprite token to die.
4. Result: Because you played your Ambush unit before the "Temporary" trigger finished resolving, you never lost control of the battlefield. Consequently, you maintain your unit presence and successfully score the point for Holding the battlefield.

According to RiftJudge FAQ #6560: "The hidden unit being played resolves before the temporary unit actually dies, so you never lose control of the battlefield. ... You maintain control throughout and score the point for holding the battlefield." (Note: While your question mentions Ambush rather than a "hidden" unit, the timing logic regarding the chain and "Temporary" resolution is identical).