Is a battery that generates hydrogen, is that very explosive

The answer is yes!

Hydrogen gas is generated as part of the charging process of lead/acid cell batteries. If the hydrogen gas acculates in large concentrations in a building or room or a box, an electrical spark or other ignition source will cause the hydrogen to burn in a rapid reaction causing an possible explosion.

A good example of a hydrogen gas explosion and fire is the "Hindenburg" disaster of the old flying blimps or zepplins.