"Body language is a part of us."
"How much a part of us is it?"
"It's so much a part of us that it's actually often unnoticed."
That's not idiomatic. It's a normal grammatical construction.
"Our clothing repairs are invisible."
"How invisible are they?"
"They are so invisible that they often go unnoticed."
Yes, you've identified one way of using 'so'. There are others which don't rely on the pattern you've identified.