No, it depends on a few things.
If it’s a fairly standard type of appointment (e.g. foreigner’s office, Bürgeramt, etc) and you don’t need someone with any specific qualification or specialisation area, then the cost won’t change.
Sometimes I might be dealing with complex information, legal content, or a topic area for which I need to do a bit of advance preparation. Or, the office you’re visiting needs you to bring a court-sworn interpreter. If that’s the case, the fee might be a little bit or a lot higher.