Arya's storyline has felt all kinds of wrong to me this season, as I'm sure everyone here has already picked up on. It feels too neat and clean, in a very un-GoT sort of way. Maybe I'm mixing up the lore of the books and the show, but I recall it being made very clear that the Faceless Men are not there to teach assassination skills to people who are "just passing through." They regard what they do and how they do it as a solemn religious duty, and the abuse of it as sacrilege. I don't see them letting Arya go, I really don't. Well, let me put it this way - I highly doubt it'll be as amicable a parting in the books.
unless the faceless men never intended to make arya a faceless man in the first place. i don't buy that arya stark just happened to cross paths with jaqen in westeros. i think the faceless men went looking for and found her.
the actor who plays jaqen basically said as much in an interview, and it also makes a lot of sense in terms of what we know about the faceless men. here's an example: jaqen sends arya to the docks for her first assignment, and when arya asks what she's looking for, jaqen replies that he wouldn't send her if he knew what she would see. when arya reports back, jaqen clearly knows all about the lender, and when arya points out that he obviously
did know what she would see, he basically says that it was a play on words; he knew what was waiting, but lol didn't kno if ud see it or not. in other words, there are lots of hints that the faceless men, either through observation and deduction, some magic, or both, are keenly aware of at least some future events. in this books this is even more clear with all the stuff about their obsession with collecting information.
in other words, i think the whole point of the faceless men trials was not to get arya to become no one; it was the exact opposite, to equip her to be arya stark of winterfell. she's vital to the endgame.