Yep, if you download all four of the mods mentioned, the Genshin Impact OST does play in the background. Since Gacha Redux used Edition as the base, and Gacha Star (updated version, before it used Glitch as it's base), Universal, and Lavender used Redux as their base. As it seems like the mod creators don't change the OST to make it less obvious another mod was used as the base, unlike the mod creator of Gacha Boba (which also used Edition as it's base, but the BGM is Lo-Fi).