Fans are pretty succes based, and this would make strong teams even harder to beat, and inn leagues like mine* it would become a big advantage to have a cup game before a home game. In the last cup round you could maybe say the opposite ;)
* a lot of supporters and nearly everyone could beat everyone ;)
Would it only help the "big" teams? Yes and No...
I would say especially the big or "old" teams, because the amount of visitors is mainly based on the home crowd and your succes(you could see it fine in the first cup rounds, with first leagues teams playing against noobs the attendance don't drop)
At home: it would, because they'd get the larger bonus from higher attendance -- but isn't that how it is in real life.
In real life their are are other factors too, like the fan club(my home club got pretty lame fans) etc.
But this is an game, so it should be important that it still make fun :) And if somebody with a winning streak becomes unbeatable at home, and a other player looses a lot of his home crowd because of a loose game i doN't think it maximumum fun which is more important then reality.