Imagine if the answer was a simple yes: adding a disclaimer was enough to exempt you from any and all copyright and trademark law suits. If that was the case, there would be no point in copyright or trademark law at all, because everyone could just include this disclaimer and never be sued.
That doesn't mean every disclaimer is useless, but it does mean that copying and pasting some vague wording without understanding what it means is very unlikely to help you very much. The example you give is a good example of doing just that; the terms it uses are real, but they've clearly been thrown together without real understanding:
- Copyright is the right to control and profit from a creative work. This is relevant because images of Pokemon characters created for games, manga, etc are copyrighted by their creator.
- Trademarks are words, symbols, images, etc exclusively associated with a particular company or product. Trademark law aims, among other things, to avoid customers thinking they are getting an official product when they are not.
- "Nintendo" and "Pokemon" are both themselves trademarks. They are also the names of different companies. My limited understanding is that "The Pokemon Company" will be the owner of all the copyrights and trademarks related to those games, manga, etc. Naming them is a way of showing that you have researched this and understood their rights.
- "This app is not affiliated , endorsed or supported by Nintendo in any way". This is a disclaimer on the trademarks. Whether this is sufficient to protect against claims of counterfeiting depends on how prominent it is compared to other branding - you need to make it obvious to users that the product is unofficial, not bury this in small-print for the lawyers to find.
- "also some images used in this app are ... supported under fair use" - fair use is a US legal concept which allows copyrighted works to be used in certain specifically limited ways. Saying your use is covered does not make it true, you need to actually understand what provisions of the law allow your specific use.
- "no copyright infringement intended" This is a fluffy apology that has no legal standing. A more useful statement might be "every care has been taken to adhere to copyright and trademark law, if you notice a violation please contact X"; but you're still relying on goodwill, and it won't stop someone sending the lawyers in if they decide to.
Which brings us back to the real question:
The apps mentioned before are in the store since 2015 and they haven't been removed yet.
The real reason for this has nothing to do with the poorly-written disclaimers, it is that Nintendo / Pokemon co haven't bothered. If an app is directly competing with an official app, or receiving a lot of attention (even if no money), the lawyers will descend; if it's a buggy image gallery with a dozen downloads, they might decide they have better things to do. If they do notice, they might just get Apple and Google to de-list the app, but not spend the time and money pursuing a legal case.
On the other hand, at any time they might decide they need to tighten up control of their intellectual property, and make an example of a few authors picked at random. The only way to avoid that is to actually avoid violating their rights, rather than just saying so in a disclaimer.