They raised just North of a billion dollars [0] in September, the 2nd Ave Subway is expected to cost $4.5b [1] for 1.5m of track, three new stops, and a new entrance at an old stop. So yea, you can be sure as shit they're not building their own tunnels. At least not here.

[0] - https://www.crunchbase.com/organization/uber/funding-rounds [1] - http://money.cnn.com/2012/05/31/news/economy/nyc-subway-cons...