A demon may Boost for less dice than its full Power (unless there's some locally-customized understanding of demons/abilities that precludes that), but no matter what, whenever Boosting to any degree, the demon's Power drops to 1 for all other abilities and other game-functions of that score. [1]

Boost can hurt.

See page 76 and 77 of the main rulebook. It's possible for a normal-to-weak person (assume a Stamina of 2), to suddenly get a Boost Stamina and become some big bad motherfucker (suppose a Power of 6, so he jumps to a Stamina at 8(!), which can cause all sorts of damage to the body, as per the rules (in this case, 4 successes on the Special Lethal Damage chart). It then becomes a question of how much your body can endure through a Boost before tearing itself apart.

Cross-reference

You can use the same "Damage from Boosting" rules for Possessor Demons utilizing their own Stamina rather than the host's if the Demon's exceeds twice the host's score (Note that this ability to supercede the host's Stamina with their own is why Possessor's don't have Boost itself.)

__Applying Boost in combat__

A demon has decided to boost its mater's Stamina this round. When does that Boost apply?

Boost is generally more... unpredictable in combat circumstances than people think and may be the most mis-played rule in the game. It is often interpreted to be a "Currency-breaker", though it is not.

1. To start, the demon rolls Power to see when the Boost occurs, along with everyone else taking their actions. The value of its highest die rolled determines when the bonus dice "hit."
2. If the demon rolls higher than the person it's Boosting, that character's action occurs when it would have occurred (set by the dice the player rolled for their character), but the demon's dice (which are sitting right there on the table) are now considered part of that roll for the purposes of determining success. The player's dice are now better than they were and better than that character's place in the line-up would have indicated.
3. If the demon rolls lower than the person it's Boosting, the Boost hits after the character has taken his action that round. Not only is it "wasted" in terms of that action, this usually means the highest die is usually not stellar. Regardless, if the next round continues on in the altercation, that Boost does apply to the character's next roll (if he or she is using the right score for their next action). Just leave those dice sitting where they are and when the character rolls again, they get added in. In many cases, they're still a benefit. [2]