Yes, carbs are also important. But if your body is lacking in necessary amino acids, its going to break down muscle to get them...
Again, you are going to lose some muscle ANYTIME you lean out, regardless of your diet.
Some amino acids will be converted to glucose if carbs are needed, so protein can provide the carb support as well...
But amino acid metabolism is a bit complicated to get into here. Take a look at the glucose-alanine cycle to see what I mean...
actually here -
So, the answer to your question is yes, but not how you think...
or something to that effect.