Yes and no.
So let me try and break it down as it's really not simple.
Imagine the superpowers as a Mob gang.
At the top there's the Don and he has all of his local mob bosses running each minor faction. Impress the local bosses and they pass on the good word to the Don at the top. It's better to have multiple local bosses vouching for you but if you get one vouching enough it'll still work out.
You can be allied to lots of local factions without being allied with the superpower and you can be allied with the superpower without being allied with all the local ones. They influence each other but aren't a direct linear relationship.
In short you can move on and it'll have more of an effect but if you find a really good place to get reputation then it'll still work, it'll just take slightly longer. My advice is to stay as finding good places isn't easy.
Rank actually has a whole separate thing though, you can rank up without being allied, there's a separate % bar on the first tab of the right hand panel, scroll through and it'll show the Friendly/allied % and then the rank and % to next rank.