Yes 100 amp electrical service is enough amperage for running a central air conditioner.
Most central air conditioners use between 50 to 60 AMP of electricity but use a bit more upon startup.
I have 100 amp electrical service to my home and I have one central air conditioner and it works just fine.
I do notice a light dimming of my lights when I have other electricity being used when the central air conditioner starts up.
But the lights return to normal soon after the central air conditioner starts up.
Mos new homes are built with 200 amp electrical service and if you have 2 central air conditioners supplying the house then you would want and need 200 amp electrical service.
For example if you have a 2 story home and need one central air conditioner for the lower half and another central air conditioner for the 2nd half of the house then 200 amps would be needed.
if you have a new home built the new home is built and supplied with 200 amp electrical service.
We now use more electricity and amperage than we used too.
At one time houses at 60 amp electrical service which at the time was more than enough but now 60 amp electrical service would not be enough and so we have 100 amp to 125 amp service.
But some homes have 200 amp service which is sometimes needed.
I plan to upgrade to 200 amp electrical service by next summer which I can do myself.