Yes and no - It all depends on the repeater! Some are on batteries and/or generators, and obviously they will stay up, so are not, and they go down. Of the primary freqs ARES uses in NYC, about 25% are on backup, including one with citywide coverage

Now, one of the things we train for is "simplex" operations - aka, direct radio to radio with NO repeaters. Not that big a deal, just don't try to go from, lets say the Bronx to Staten Island with a 5 watt HT and a rubber duckie antenna - It's NOT going to happen. Heck that going to be a stretch even with mobile units - but people will relay your traffic

On HF, that kind of distance is "trivial", and in jact, depending on antennas can be to SHORT (due to skip)

To give you an example - I live in the FAR NE corner of Queens - I can get my signal into most on Manhattan, the Bronx, MOST of Brooklyn, and small parts of Staten Island, along with oh, 85% of Nassau - enough that I can reach repeaters in all but Staten Island. Depending on what kind of antenna and power you are running, you may reach me from those same spots, SIMPLEX

We had no problems keeping at least 3-4 repeaters on the air during the last balackout in NYC alone, and a lot of the stuff in Nassau was up (they have more sites with batteries than we do, simply because of space - room for batteries in repeater locations can cost BIG dollars and is usually NOT available on a donation basis)