Lucky Powers +++ and S give an extra shiny roll during every encounter, as well as increasing the chances of finding Pokemon with low encounter rates, and decreasing the chance of finding Pokemon with high encounter rates.
Since you can soft reset Pass Powers to use them again, you can continue to have boosted shiny odds as long as you keep soft resetting.
I'm just asking to verify if that doesn't tamper with RNG and I can find the shiny eventually by soft resetting
It's very difficult to "tamper with RNG" in Pokemon without knowing what you're doing, (See RNG Manipulation). You can always find a shiny eventually, so worry not! You will eventually find your shiny.
Hope this helps!