The US, like Russia, has been placing human intelligence assets throughout the Ukrainian government and military since 1990. (They even recruited two native Ukrainian speakers right out of my high school, one of whom later went on to become an astronaut instead.)  This is the one place in the world where the US may actually prepared for something intelligence-wise, but yes, clearly it would require a sounding from Ukrainian generals that they are against the Russians. (And perhaps they've already sounded and found lacking, which may be why we haven't seen anything like this yet, since is otherwise exactly the the thing NATO forces have been training for in Europe since the fall of the Warsaw Pact.)

There are always choke points in transit routes where it is impossible to push past -- bridges, tunnels, cut passes, etc.  Those are where units from both sides would be racing to get to first, but NATO only has to reach some of them to be successful. Russia would have to capture nearly all of them because it is the side that has to move in a sufficiently large invading force.  NATO's objective would not be to defend eastern Ukraine against Russian forces, but merely to force the Russians to have to kill some Americans to get by.  Russia actually needs to insert a full army into the area to be successful if the Ukranian army looks like it won't stand down.  As long as NATO can reach some of key sites first, it means Russians would have to shoot to move them to secure a position capable of defending against a possible Ukrainian counter attack.  Since Russia would be the invader, NATO can shoot at Russians even, without the same consequences, and NATO would be betting on Russian beliefs about notoriously trigger-happy American troops for this kind of poker stand-off anyway.  

It's really just classic Saul Alinsky with armed forces instead of civil groups:  Get a some people in the way and force the opponent have to deal with the problem, a strategy that Putin himself has already mastered and thus completely understand if he's been outplayed at it.