No and yes.

Objective characters are not a single group of characters working in concert with one another. There are many factions, as well as many varied functions performed by the various characters. They never all have the same agenda. In fact, as much as the protagonist works toward resolving the OS Problem, the antagonist works against its resolution.

The bulk of the objective characters are not aware of the Overall Story Problem and OS Solution until the last act of the story. Some may never be aware of them, even after the story is over. They might see them but not recognize them for their importance. Others may never be aware of the OS Problem and Solution, seeing only the OS Symptom and OS Response.

There will be one or two or more objective characters peppered in the story that can see what is going on, or at least partially so. They provide the voice drowned out by the crowd of other characters that gives insight into the story mechanisms that drive the Overall Story throughline. Sometimes it is the protagonist that does this (e.g. Atticus Finch in To Kill A Mockingbird), sometimes the Guardian character, the Antagonist, or a combination of characters (e.g. Obi-Wan and Princess Leia each have incomplete, privileged knowledge about what is really going on in Star Wars: A New Hope).

Even then, these characters may not know about the OS Problem and Solution until later on in the story. Like the Main Character development, it is not a matter of being all or nothing, but a matter of WHEN they know -- or suspect -- what is causing the troubles. Unlike the Main Character development, the Overall Story throughline present the logistical problem to be solved. Instead of the layers of justifications blinding the MC from the source of his troubles, there is a Story Goal in the OS throughline, with Requirements, Prerequisites, Preconditions and more to wade through in order to achieve the Story Goal while resolving the OS Problem.

Lastly, there is the matter of when the AUDIENCE finds out about the OS problem and solution. That is mostly a matter of storyweaving -- controlling WHEN essential information about the storyform is revealed to the audience. There may be a difference between when the characters know, and when we, the audience, know, and when we know THEY know. Fortunately, it's up to us as authors to make those distinctions as we see fit.