It depends upon the content of question and answers. Let's see some examples (similar to that illustrated in the question)
Question: What is the story of Damayanti marrying Nala?
It can be possible that the stories found in different scriptures have some variations. So, it would be useful if answers are posted from different scriptures.
Question: What are the scriptural source for Damayanti being a wife of Nala?
If the question is looking for scriptural references, posting multiple answers citing different scripture is obviously adding values to the site.
Question: What is the name of the wife of Nala?
This doesn't look like a good question. It looks trivia/quiz type question. If an answer is already posted like "Her name is Damayanati..." citing Mahabharata", then it would not add much value if you post more or less same thing citing different scripture, however if you can add some more details (e.g. about Damayanti or story of marriage) apart from what contained by existing answers, then do it. It will help the site and visitors.
Touching the title of question:
Does proving same answer from different scripture helps the site?
Well, it will help if the question is looking for proof e.g what mentioned in the second example above.
The thing to note down is: If your answer is not adding anything extra or different things from the existing (already posted) answers, then it will not help the site but if your answer contains some extra information or trying to explain the thing with different aspects putting little more efforts, then it will definitely add value to the site.