If you use PM standards such as the PMBOK standard of the Project Management Institute (PMI), does this warrant that your project will be successful? Unfortunately, the answer is no. For me, the PMBOK is a toolbox, and depending on the requirements of the project, I use some tools, and some tools stay in the toolbox. It is comparable to the real toolbox that you might have in your house: You carry this toolbox with you if you have to repair the water tap and if you have to repair the car, but you will most probably not use the same tools out of the toolbox in both situations.
Now, using this picture, if someone does not possess the PMI toolbox, does it mean he does not have the tools to work on a project successfully? No. Actually, some of the PMI approaches are common ground with respect to other disciplines, even if they are labeled differently. Using a project log, for example, is not a PMI-exclusive approach, and it may be called differently in other domains. Managing stakeholders may also be the outcome of common sense. In other word, you can be successful in project management if you don’t have any knowledge of the standards. However, having the knowledge will not hurt you; in fact, your work might be easier if you are aware of best practices and available tools; if not, everything may look like a nail because you just know the hammer.
On the contrary, if you can be successful without the PM standards knowledge, this does not mean you will always be successful just by using PM standards. Just because you know that there is such a concept of managing stakeholders, this does not mean that you will do this successfully. Your communication strategy may be suboptimal, politically-based actions from others may ruin your project plan: There is more than just the PM standard that should be followed, and this is the non-reproducable part of project management success: The project manager and his soft skills that are not standardizable. Still, an untalented project manager may be more likely to be successful with a PM standard since he is using best practices, but it will not be a guaranty.