Plants usually make it through a blackout doing okay. Obviously it's not something you want to do routinely to them, but on the short term, they usually come out of it all right.
They will come out fine, but you really need to determine the reason for the green water or you can/will have a re-occurrence of the green water. Seek your water's balance and get the plants growing well once you've finished the blackout.
For a blackout:
Do a 50% water change.
Turn off the CO2 and raise spray bars if applicable.
Cover the tank completely for 2 days.
Uncover and do another 50%er......do not feed the fish(they will be fine) and recover.
Cover again for 2 days.
Uncover and do another 50%er.
Find your balance of nutrients/fish and light to avoid a re-occurrence.