You are probably right. We already have 14 cities, whereas judging by the diplomacy screen, other civs have:
Arabs - 5
Spanish - 4
Persians - 6
Russians - 4
Romans - won't talk to us
French - 3
Inca - 1
So we can probably overwhelm everybody else with production already.
So it actually makes sense, I guess, to let them settle the new world and slow down their own economy. Especially since we are wonderless, and hence don't need no fancy buildings like Versailles or Forbidden Palace.
Hence, it would probably hurt us more than help us to grab the majority of the new world. Still would be nice to be the first to explore it, if only to pop some of those huts.
Hey, you never know, there might be
a tech on one of those!
Free money never hurts either, I think we have survived ever since the beginning of the war on Inca on money we've pillaged from conquered cities. 
Vovan
PS: I just thought of something else, too, it might be a good idea to switch to Hinduism now.
That way, the Arabs and Persians will like us more, since that's their state religion, and might be more inclined to trade us more techs. Also, we'll reveal some of the map, since they probably have some Hindu cities, and we now have a Hindu shrine. 
And also another thing: we have open borders with Persians and Arabs (east of Madras). Probably a good idea to send some Keshiks into their territory, just to see what they have.
Arabs - 5
Spanish - 4
Persians - 6
Russians - 4
Romans - won't talk to us

French - 3
Inca - 1

So we can probably overwhelm everybody else with production already.






Vovan
PS: I just thought of something else, too, it might be a good idea to switch to Hinduism now.


And also another thing: we have open borders with Persians and Arabs (east of Madras). Probably a good idea to send some Keshiks into their territory, just to see what they have.