Not just in terms of self-fulfillment:p:p:p, but a game that will actually contribute to reasonable financial gain. Is there any real world examples in App Store?
Unity Basic is as good as the user. The limits are rather tame and likely the only big “issue” is that you must have a splash screen with the Unity logo (not really a bad thing, after all UDK games tend to brag about using UDK and keep the logo up all the time, why not do the same with Unity?)
Not sure about any real examples of unity basic in the app store myself, but I can see anyone that makes a title successful enough going out and upgrading to pro as soon as they earn the money to do so.
The use of Pro won’t change your capabilities of making a game that can bring you financial gain. Your development and marketing skills are the real limits of how successful your title will be.
My app was done in unity and iOS basic? 
I think, it runs perfectly how I wanted so on production scale there was no issues. Just flunked at the marketing stage. App im working on now is also iOS and Unity basic, so ill quite happily (if this thread is around) get back to you febuary time.
No, as you also need a talented developer or team for a successful app. This component is way more important than the rest.
Is Unity Basic and iOS Basic Enough to Make An Successful Game?
Short Answer: Yes
Long Answer: No - (because there’s much more to successful games than the tools used to make it)
As others have mentioned the tool is powerful enough to make a “successful game”. However, like all tools, its only as good as it’s user(s). If you (and your team) are good, then you will make a successful game. That means you have to be good at making games, good at using unity, good at marketing and good at customer service you will do well. Each of those parts could be broken down further to other things you need to be good at, but I think the point is clear. The tool can make a solid game, but its up to the developers to make it successful.