No, User Interface settings are not available in apex, nor are they even available through the metadata API. The only configuration option here is to set them through the Salesforce UI.
EDIT: The one lever that you do have around Salesforce configuration in your customer target org is setting up Package and Object Requirements when uploading your package. The packaging engine is smart enough to select what's necessary from your package metadata, but you can add dependencies like Flow, Account Teams, or Multi-Currency if these instance configuration options are essential to the smooth operation of your package. I can't find any settings that are close to what you'd find in User Interface config though, but this is as close as it gets to what your talking about. More info on defining package dependencies here: