Short answer is no.
Take a look at the Facebook User object reference. Each user has a likes property that is only accessible under extended permissions granted by the user.
A user would need to have granted this application the user_like permission to the app, for the app to be able to see that user's likes. This does not apply transitively to friends of the user.
Just because there are other users of the application they will not transitively get any permissions from you. Your public profile is just that, its public. Properties under that are always visible to all users of Facebook (apps and individual users).
Clearly the app will have access to likes from all users that have granted it the user_likes permission.