Great question. Not sure of the answer but will give my opinion...
I have a feeling based on what we've seen that Emery will see the FA Cup as fairly important, but not as important as Top 4 or the Europa League. I am expecting a full strength lineup tomorrow, perhaps with the exception of Leno for Cech.
Having said that, I don't know what a full strength line-up is under Emery. He is very horses-for-courses, a lot of formations and player selections differ depending on the set-up of the opponent. For example he went with Maitland-Niles on the right wing at Liverpool, he will make odd selections like that. And the formation could be anything. 2 or 3 CBs, 2 or 3 in midfield, 1 or 2 strikers, many different options. Emery will make those decisions based on your set-up and tactics that he has observed through video analysis. Obviously quite different from Wenger who went out to try and dictate the game every single time, even in ridiculous circumstances like playing against tika-taka Barcelona at the top of their game (although incidentally a home tie against them actually did result in one of our most famous victories! The exception to the norm though when it came to big games after about 2009).
I think a successful season for us would be Champions League qualification, by way of the top 4 or winning the Europa League, either way.
However if we don't do that (you'd have to say we're not the favourite for either of those scenarios), I don't think it would be seen as a failure either. It's his first season, he will be given time.
An FA Cup win would be a lot like it was for Wenger when he won the last 3 most probably - nice, enjoyable, but ultimately not the marker of overall progress. Emery is a little like Klopp in that he places a lot of importance on the players to entertain and engage the fans at home, so that's why I think he might see this game as very important, not for the overall goal of the FA Cup necessarily. Although I did enjoy his comments about Arsenal's FA Cup history, so perhaps I could be mistaken there.
Pretty standard expectations in first season I suppose. Would expect that no CL / top four and no trophy would not be enough in a second season.
Interesting to hear that Emery is able to adapt team to suit the type of game. Have Arsenal got the players that can do that too? Pace up top and technical midfield is an interesting combination in itself.