Well not technically because everyone has different ranges that they can smell. Meaning that it could not set off a reaction unless you can smell them so i do not believe that is true. Although my friend is like deathly allergic to peanuts and if she is sitting by someone with a PB&J she like get light headed and almost faints so it is possible that being around them could affect her much not mearly the since of smell could trigger it.
It depends on how sensitive a person's nose is. I tend to smell things before others do. If the banana has been peeled I can smell it from I'd say 8-10 feet minimum. As for smelling it setting off her allergies that is quite possible. It happens with people an peanut allergies.
I'm not sure of an allergy just from smell, but I believe anything is possible. My boss absolutely forbids bananas anywhere in sight, so maybe their are underlying issues that I or others are not aware of.