Scraping HTML is fragile -- yes you can do it with beautifulsoup4, e.g
import bs4
soup = bs4.BeautifulSoup(html_string)
href = soup.find('h3').find('a').get('href')
print(href)
will show /url?q=http://www.youtube.com/watch%3Fv%3D9LjbMVXj0F8&sa=U&ei=ESCPVPD6NcT3yQS-04C4DA&ved=0CBQQtwIwAA&usg=AFQjCNGV1u7FshGW4K_Ffu0zLzwaW7sCzw or the like. However, the slightest cosmetic change to Youtube search results might break your application.
Better to register your app with Google and use the provided API, as per Google's own docs. The Python client library nicely supports App Engine, see https://developers.google.com/youtube/v3/code_samples/python_appengine for example.