That would depend. I have battery backups for my radio's and have several in the safe just in case. Antenna's won't be affected.
Lots of ham repeaters have batteries that keep em going for a day or two if they are used lightly...after that if the power dont come back on they go down. we arent talking a dozen D cells here or a box of AA's...we are talking several deep cycle marine batteries at 80 pounds each or the super expensive and just as heavy gell cell batteries.I keep 6 new 27 Series Marine deep cycle batteries a large supply of gasoline and a pair of generators...I also have solar panels for charging batteries as well.
D star depends almost soley on the internet for distance...otherwise its like a regular repeater...Internet goes down...battery backup goes down...Its done.
Cell sites and SMS have a 48 to 72 hour backup generator....During Katrina and after some cell sites didnt come up for months....During 9/11 some were out weeks. During the Oklahoma City Bombing some cell sites were out for weeks. We have local cell sites here that sometimes go out for a week just because some idiot thats too sorry to work decides he wants to sell copper!
If your a ham and only have handheld radios....you have about a 5 mile range without a repeater...possibly 10 to 15 with a good outdoor directional antenna...How many batteries you have dont really matter if you dont have a repeater or internet...If you want distance without the net and repeaters your going to have to go the HF radio.
I keep up a couple of ham radio repeaters myself.
SSGT