Short answer: No.
It helps to have an appropriate mental model of the problem you're facing. Imagine that your app is a filing clerk (program binary) working in a rented office (the user's phone). He's got his own computer, desk and phone (process running on the user's phone), but the filing system (file system) is controlled by the landlord of the office building (the user). You can trust the landlord to keep providing your office equipment, but you know they have an agenda of their own, which may include messing with the work you're doing.
The important point to see is that the clerk can work unimpeded, but he goes home every night (when the app is closed), and the next day he'll only be able to remember where he was and what to do by reading instructions from the filing system - which may be compromised by the hostile landlord.
This explains why it is ultimately impossible to guarantee a secure workflow while completely depending on a hostile persistence provider. You can leave yourself notes, but the landlord might intercept and alter them. You can encrypt the notes so that others can't read them, but the landlord can apply cryptanalysis. You can sign the notes so that they can't be altered, but cryptanalysis can be applied to that problem as well. Worse, the landlord is able to scan the clerk's brain (program binary) while he sleeps and analyse its workings, including the part where he stores the secret encryption key. The landlord can even simulate running the program in a secret environment and observe how it does the encryption (here the metaphor breaks down).
Therefore, all you can do to make your workflow secure is to try and make countermeasures more expensive. Encryption can help with this, but it depends on the situation whether you can make it expensive enough to actually prevent what you want prevented. Probably no one will employ virtualization and cryptanalysis just to generate a fake online high score in a small casual game. But you never know - maybe your app will go go viral, and high-level profiles become worth a lot of money. All you can do is estimate how much effort someone would expend to subvert your program, and plan for this amount of countermeasures.