On copper the exchange has its own battery backup and/or generator, so broadband should still work, assuming you have your own local power for the ADSL modem.
On FTTC, the cabinet has battery backup
On the floor in that picture, alas cannot decipher the Chinese data sheets.
Voice would be unaffected as the copper pair will work even if the FTTC cab is totally turned off. Broadband will keep running so long as the batteries do (think its 8 hours for a full cab) but probably longer as lots of people connected to cab will have no mains for their router at home.
Batteries can be swapped out I believe in case of longer outage, but don't think they guarantee that, though depends on the customers connected possibly.