Also current target fusion reactions are not based on the p-p chain. That is a much more difficult reaction to achieve. We're currently targeting D+T for first generation reactors. D+D is also very attractive because it is aneutronic and perhaps clever reactor design would allow for direct conversion of electricity. Energy in aneutronic fusion reactions is released as an acceleration of charged particles: a current. This current can be harvested through magnetic fields and thermal to electric efficiency can go up to 50% (maybe higher?). The actual details of this seem rather tricky since magnetic confinement devices are already tightly controlling the magnetic fields inside the reactor. It will be fun science and engineering for sure.
There are a few other commonly examined reactions, such as p+B11, but they're likely not going to be made viable reactions for energy production before D+T. These other reactions are all easier to achieve (in terms of Lawson criterion) than the stellar proton fusion chain.
I'll reuse your math with D+T=He-4+n and 3x energy production.
(4380000 TWh / year) / 17.59 MeV / avogadro * 4.002602 g/mol
= 41425784.21 kg / year
(4380000 TWh / year) / 17.59 MeV / avogadro * 4.002602 g/mol / (0.1786 g / liter)
= 231947280 m^3/year
1. as you acknowledged, the assumption that energy production would increase by tenfold
2. that all electrical energy produced would be made by fusion reactors
By the time we get to a state where a serious percentage of energy production was from fusion power we would likely be looking into more aggressively into other reactions and designs.
Even if we just said 30% of all energy used today was made from D+T fusion that would still be generating 10% of our current helium usage. That's a significant amount and a lot more than the 4 orders of magnitude that is oft cited online (https://www.reddit.com/r/askscience/comments/12r2s7/helium_i...). At a glance, it appears that the posts in this thread miscalculate how much fuel is necessary for a certain amount of energy. They glaze over that part of their calculations. I much prefer your dimensional analysis approach.
(.3 * 438000 TWh / year) / (17.59 MeV) / (avogadro's number 1/mol) * (4.002602 g/mol)
No, according to my source, it includes combustion.