I assume you mean Rare Soda, not Rare Juice.
Anyway, the answer is no; the use of the items themselves does not effect stat growth at all. However, they can still effect your Pokemon's stats. Along with EXP Points, Pokemon get EVs from defeating a Pokemon. At level 100, 4 EVs = 1 stat point in the stat the EVs are in. Since Rare Candies and Rare Sodas allow you to get experience points without participating in a battle, the Pokemon won't be getting EVs.
So really, they are just a less efficient way of levelling up a Pokemon in terms of stats. They do not have any negative effect. They don't halve stats, they just don't give you any EVs.
If you are unaware of what EVs are, read up about them here.