If the FA Cup winners finish in the top five, which appears to be the case, they will qualify for the Europa League. The other 16 places at the play-offs will be given to the FA Cup winners, as well as the league runners-up who were not already qualified through their league position. Qualification would cost them because they only have one spot available for Europe. But if they win the FA Cup again, then they'll get another chance in 2018. The FA Cup has been used by European teams as a route to the Champions League for many years. In 1995–96, Chelsea made it to the last four of the UEFA Cup after beating Liverpool in the final. In 2014–15, Manchester City reached the semi-finals of the Europa League. Both these teams had finished below Chelsea in the Premier League that season. So, yes, winning the FA Cup does guarantee qualification for England's football team.