Actually... it does. A lot. In a team game it would be ideal to have the guy in the back (Inland Sea or Donut) playing with the religion. Usually he is building the Wonders (Org Rel) & has the bigger cities because of less whipping. He also would have better opportunity to spread the faith, as compared to someone on the front lines. Now we know we can research up to '1 turn' and have everyone switch off to the next tech while the desired person gets the religion. Pretty sweet.
I'm glad it helped
The only flaw is not all people are equal...AND 3 people are greater than 1. If 3 people researching together can discover Polytheism in 1 turn, then 1 person alone might take 5 turns to discover Polytheism. Also what if your enemies are also focusing on Polytheism? If they are, chances are they'll get the religion before you.
Any idea if there is some kind of programming against religion-hording? It seems that any subsequent religions seem weighted to go to teammates without a religion already.
Ex. If we all research Meditation, I get Buddhism. We all switch to Polytheism and Teammate 2 gets Hindu. Not sure if that is simply fluke or not, but it seems to spread it throughout the available teams. Just luck?
I've done some basic testing, and there is no coding against team-mate religion-hording. Only city-religion-hording. Meaning:
1) If you have 3 religions in all your cities, and your partner(s) has zero religions in all of his cities, and YOU found Confucianism, the religion will randomly go to one of your cities.
2) If you have 5 cities, and 4 cities have 5 religions each, the 1 city with 0-4 religions will be the new religion's Holy city.*
3) There is a common misconception that religions need roads connecting and/or open boarders to spread. This is
false. Religions WILL spread without roads connecting, and without open boarders.**
*I have not extensively tested this, and I might be wrong.
**I have been playing as Isabella due to her starting tech a lot lately. Fishing = research, and her other tech gives her the research boost. I started a new Prince game to try a few new strategies, and ended up with an awesome starting location. Had two crabs right next to the city, and two fresh water lakes in her BFC, along with other goodies on land. Regardless, two crabs + two fresh water lakes = I got Buddhism and Hinduism before the computer players. I had slow production, but I ended up with all 7 religions in that one city by about 1000 AD. Yes, I managed to make a Holy Holy Holy Holy Holy Holy Holy city.

I still have the 4000 BC save if you'd like I could upload it here for fun. I digress...Regardless, even without open boarders and sans roads connecting my civ to others, my religions were still spreading. They seem to spread much quicker with roads and/or open boarders, but even without, they'll still find their way into enemy territories. I think it has to do with cultural boarders touching, but I'm not 100% sure.
Good luck.
