Does "sink down" describe that someone who is tired and exhausted sits in the chair?
Dorry sank down in the hard plastic chair as if that would make her invisible.

Does "sink down" describe that someone who is tired and exhausted sits in the chair?

and then.. as if that would.... what does "would" mean?

I think would in the context mean what someone believed, hoped, or expected to happen"

is it right?

Question

Does "sink down" describe that someone who is tired and exhausted sits in the chair?
Dorry sank down in the hard plastic chair as if that would make her invisible.

Does "sink down" describe that someone who is tired and exhausted sits in the chair?

and then.. as if that would.... what does "would" mean?

I think would in the context mean what someone believed, hoped, or expected to happen"

is it right?

Answer

Yes, you can sink down in a chair if you are tired.  But I think that in this case the person is feeling shy and uncomfortable, and doesn't want to be noticed. The 'would' is a type of conditional, based on 'as if', to describe an impossible or imaginary situation. Sitting down can't really make you invisible, but she sat down as if it 'would' make her invisible.

Answer

Your  analysis was right.  "Does "sink down" describe that someone who is tired and exhausted sits in the chair?"  Indeed.

Also,  another phrasing that is sometimes seen is like this.

"I did not want to sink down into a pit of despair."

It means of course, I did not want to feel confused or depressed.