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In theory you can fuse up to Iron.... the last stage of stars. You are not limited to just Hydrogen.

takes a star's worth of gravitational force to push atoms like those together in the core to produce fusion.

To reproduce such heavier elements in fusion reactors on earth would require, likely, a much higher energy than the output.

I assume that some of fusions done by the star are net energy consumption (i.e. not usable for energy production)

You assume wrong. Anything beyond iron is made in a supernova, i.e. in the last moments before it is not really a star at all, anymore.