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I think far less efficiently than propelling a light sail - asteroids being not very reflective. There would be some momentum imparted by the photons impacting and more by ablation of the surface though (if the laser is powerful enough).

Enough to deflect? A kiss from a kitten is enough to deflect if you do it far enough in advance…

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To divert an asteroid, you’d attempt to ablate a part of it, rather than just rely on its reflectivity:

https://en.m.wikipedia.org/wiki/Asteroid_laser_ablation

I imagine that tracking an asteroid and continuously pointing the laser array at a specific portion of it, will be harder than tracking a shiny light sail that’s continuously illuminated by the laser array—but as a whole, I think shooting a laser at an asteroid is one of our best bets, so having that array would be a good tool of planetary defense

I like the idea of diverting an asteroid by firing kittens at it.

Your idea of kissing is a bit violent.

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