If you miss a train for which you have a ticket, generally you can go as a standing room passenger on a later train that day, if there is space. You can grab a seat if there are vacancies, but if there aren't, you'll be standing for 2 1/2 hours.
What's your secret for arranging previously purchased train ticket pickup at NRT? I guess your friend could be there waiting to hand them to you, but other than that, I've no clue how one does this. Maybe a guru can elucidate.
Personally, I'd take the risk and go for the flight. You could be 2 hours late and still easily make it, especially if you don't check bags and hurry to immigration on arrival.