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…
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
Interesting, I was thinking of them for another use as well: dumping surplus photovoltaic/wind collected energy into space as a thermostat of sorts to help control global average temperatures and buy more time to handle CO2 emissions. Not sure but maybe its cheaper than using batteries for time-shifting that energy to reduce fossil fuels during the transitionary period.
Enough to deflect? A kiss from a kitten is enough to deflect if you do it far enough in advance…