Ya you can build muscle without carbs but as many ppl mentioned above, carbs do produce an insulin response and insulin, especially post workout, increases protein synthesis rates.

That being said, there was a study done looking at protein synthesis rates pwo with either 30g or 90g of carbs consumed and the insulin response was the same, so you dont need to an absolutely crazy intake to capitalize on this. Secondly, your carb intake should correlate with your current bodyfat percentages. If you are sitting at 20%+ bf, then id keep the carbs to a minimum until you get yourself down to a reasonable range. The leaner you get, the more carbs you can/should have.