I am trying to build a service which would search across Google, Twitter, Youtube and other sites to get content relevant to a particular topic and provide it on one screen to my users ( like a meta search engine)
They sure will. Google even has an API for this( https://developers.google.com/custom-search/docs/structured_data#overview ) as does Twitter, YouTube and probably the other sites you are looking into. The major problem you will have is the limits and these services will get pretty expensive fast if you reach them. I would look into something like Apache Solr or Elasticsearch to help you store your results so this is less of an issue. Good luck!