In Ticket to Ride USA, does obtaining longest continuous path of routes highly correlate with winning?
Yes, obtaining longest continuous path of routes certainly does highly correlate with winning.  It's pretty simple to see why:


Multiple routes that "cooperate" by overlapping are obviously more efficient than short routes in different parts of the board that have nothing to do with each other.
Longer routes are vastly more cost-effective than short routes. A 6-length route takes you one turn to put down and earns 15 points. 6 1-length routes would take you 6 turns to put down and earn a measly 6 points.
As if the inherent advantage of playing long, complementary routes wasn't obvious enough, you even get an additional endgame bonus for having the longest continuous path!


As I suggested in my comment though, you don't have to roll over and let other players build long, efficient routes at their leisure. In my group, sabotage tactics are very common, and if someone  obviously has designs on a long, efficient chain of routes, then building obstructively, or just picking up the colours they have telegraphed they will be needing to collect, can really ruin their day.

I also mentioned what is possibly the strongest deterrent to building long, leisurely routes: the capacity for a player to speed up the end of the game by going out quickly.  The lucrative Los-Angeles-to-New-York mega-route in your hand becomes a huge liability if your opponents block a few key connections in the midwest and then play to run themselves out of trains as quickly as possible.  

As such, it's not always good to have a hand of long, valuable, complementary routes at the start of the game: a couple of seemingly unambitious short routes may be enough to win the game, if you play to go out as fast as possible and are the only one to have completed all the routes in your hand.  Lumbering your opponents with big negative points can be just as good as working hard to score those points yourself: all's fair in love and trains...