Hi Lim, good question.
I also mainly use a drinks fridge to age my cheeses, not good as 1) too cold and 2) it's a forced air fridge so air is highly dehumidified. I get by as Debi says, using plastic containers.
To answer your question, the fridge does smell, but as only cans of soda and bottles of wine it's not a big deal to me, I'll ask my wife when available.