You'd be surprised.
During the Mumbai floods of '05 we had landline connectivity till almost 8pm ( the deluge had started around 2), and mobile phones worked till about midnight after which their backup generators ran out of diesel. Power had gone since about 4pm, as the water level was already above the distribution boxes. Those from Mumbai will remember: most highways in the suburbs were under 8 feet of water due to the cloudburst.
As it may be, after the rains cleared on Wednesday evening most of the city was back online after midnight. Thursday was almost normal and by Friday everybody was in business. We had to launch a newspaper on Saturday, and though we had only two days to do it as against the two weeks it normally takes, we managed to do so.
And anyway, you wouldn't mind a week or so delay in getting all your important documents back, even if it did take that long. Physical copies are less safe because they tend to be useless after a bit of water contact.