Giving you exact number would require knowing the exact numbers beforehand. The probability of a single item being (or a particular chest containing) a cosmetic doesn’t change, but you get double the chances for the same effort. This does raise the chance of getting one for each “unit” of effort you put in (but that’s not really possible to measure), but by how much, I cannot say without knowing the original numbers. What I know about probabilities tells me that it almost doubles the chances, but not quite (and the smaller the chances are, the closer to double it is).
It’s still unlikely, anyway, and doubling a small chance is still a small chance. If the chance is 1%, getting two rolls for the price of one isn’t going to be felt much (changing the chance from 1/100 to 199/10 000, if I calculated correctly)