Well, adding calcium sulfate as a dose would raise the general hardness of the water (GH), and sulfate content of the water.
However, you're not talking about adding calcium sulfate.. You're talking about adding sulfuric acid to water that already has a lot of calcium in it. In this interaction the hardness stays the same.
All you're doing with sulfuric acid additions is:
1) driving down pH
2) driving down KH (and producing CO2 in the short term).
3) increasing sulfate
The interaction of the sulfate with calcium is irrelevant, as in solution they're both effectively free ions and the calcium was already there,
Generally speaking, having incredibly high sulfate content isn't a very good thing, but within any kind of sane limits the extra sulfur is just plant fertilizer.
The reduction in KH (and buffers in general) would be something that I would be keeping an eye on, too low there and it can destabilize pH.