when NoSuchElementException is thrown - is it correct behavior or not? If it isn't correct, don't catch the exception. There is a method called checkIfElementOnPage(WebElement element) in BasePageObject which checks if given element is present on page or not. Inside this method we change the implicitWait so you don't have to wait. This method returns true or false.
What is more if the exception is not thrown you are not setting implicitWait time back to default value.
One more thing, if you want to mark something as incorrect inside PageObjectLogging.log() method last argument should be false not true.