Depends on your definition. It seems Neptune-type planets are either included, or not included, varying from speaker to speaker. They’re mostly volatiles, as opposed to what we’d call “rock”, and do have H/He right at the surface. But, it’s largely ammonia and water underneath, instead.

Matter in the universe is 98% hydrogen and helium (as of the current billion years, anyway). Any strong enough gravitational field is going to end up pulling in a lot of it. Smaller fields like ours tend to have trouble holding on to it, because it doesn’t take much solar wind to blow it off. So, yes, any Jupiter-sized gas planet should have that composition. Although, there’s at least one known example of a former, or maybe potential, gas giant, that’s been stripped down to it’s core.

Public service announcement that when you vent helium into Earth’s atmosphere, it blows off into space forever, and we’ve used up a lot of the stuff already.