Does your Pokemon evolve if you black out in the fight where it levels up?

Solution 1:

After performing an experiment with a volunteer Pidgey, I can say: You will not get the chance to evolve Rufflet if you lose the battle.

The experiment:

1. Level 14 Pidgey, Level 100 Bronzong, Level 100 Heatran.
2. Lead with Pidgey vs. Level 71 Sharpedo.
3. Swap in Bronzong and explode.
4. Pidgey gains 17 levels.
5. Swap in Heatran Explode.
6. Swap in Pidgey and faint.
7. Rapida blacked out!
8. Wake up at the poke center.

No Pokemon were harmed in the making of this experiment.

Solution 2:

No, you will not.

But, if you level it one additional level and win that match successfully, your pokemon will evolve.

Solution 3:

You will not get the chance to evolve Rufflet if you lose the battle.

If that happens, use a Rare Candy (if you have one) to give Rufflet an additional level. Rare Candies can evolve Pokemon, if they are at the correct level.