Yes, the perfects aren't stored in the passwords. The only thing stored are the bosses and the number of E-tanks.
There's actually the possibility to get more than 4 E-tanks before the Bison stages due to the fact that the E-tanks respawn after using a password. However, the password only can store 4 tanks at max - it's the same password system as in Mega Man 2 for NES.
However, you still can get Akuma even when starting direct at the Bison stages by defeating the right bosses there.