Of course, over time people on this side of the Atlantic will gain brand awareness, especially if they go all in with a huge, costly advertising campaign. However I think you're mistaken that anybody without an interest in aviation pays any attention when passing through an airport. If you asked 20 people in a UK high street if they'd heard of jetBlue today, one would probably say yes, 17 would say no, and the other two would probably say they flew with them from Manchester to Tenerife last year. Their brand awareness would increase slowly over time, but to say it's "bye bye Norwegian" the minute they choose to fly into Gatwick is moronic.
I agree that for many, it will come down to price. LON-NYC/BOS fares are already low, so undercutting the vast amount of competition in order to increase market share probably won't make jetBlue any money.