To followup on whether corps can help you win faster, I am going to relate briefly my current game.
Playing as Julius Caesar. On a continent with Tokugawa who I cut off with a well placed city (Thankyou Snaaty). Toku had room for only 2 cities, then he settled off continent. I took those cities with Prats, then proceeded to peacefully expand in the other direction, getting alot of well placed cities.
At this point I essentially have an isolated start since Toku will not open borders. I build Swan Palace and adopted FR very early.
Since Toku is so lovable, he refused open borders with the other 5 AIs who were actually within galley range of myself. Since they were Monty/Khmer/Isabell/Roosevelt/Justinian they all hated each other and were thus in open warfare, tanking their teching abilities. When they finally found me it was obvious I had an easy chance at a space race win (all were cautious because of the early FR and example that the Swan palace can be a very useful wonder). I had Rome going well for wonders, Antium as a GP farm (with GL), and Kyoto with some wonders and hermitage to force Toku's cultural borders.
So where does this fit in with faster corp wins? We know it takes time to tech and build the SS. I managed to get a GE and GM which I used for Mining Inc (3 times production of Creative constructions) and sid's. I spammed all religions post factory and mass building culture. It is amazing but looks like I will obtain a cultural victory now alot faster than the SS I was shooting for. Each city is 1/3 of the way to legendary and I have not used a GA, nor swung the culture slider up yet (waiting to tech mass media).
The +11 hammers with factories/powerplants allowed very fast temple/cathedral construction and sid's offers lot's of food for specialists and culture. This is helping me win faster both in game time and real time.
Corps rule!!!!!