I doubt they will be surprised. Bear in mind that many people in Europe who live outside the EU want to be part of the EU. Polls show that quite consistently for the UK, too. (Though, to be fair, you could easily ask the poll question in a way that would give the opposite majority.)
Speaking as one, they usually are. I mean polling is mostly BS, all the polling said the that UK was staying in the EU even as the voting opened - look how that turned out. Actually the polls were about the same (~65%) as the polls in say france today which say 68% in favour of EU membership - so could I say france wants to leave the EU? All total rubbish.
