Not if it’s a tank system. They can, but they don’t have to, since the pilot stays lit all the time. A tankless system has to use some power since it cycles every time you use it.

My gas hot water heater does not have an electric start.

None that requires the house electricity. Piezo, batteries easily work.

Some use a 9v battery on their starter.

Regardless, you can just use a match if you want to.

In either case, they don’t require mains power.

(Sure, there are different models, etc. but it’s not a requirement that all have an electric start, or a mains electric start)