You can but cedar and other wood mulches tend to leach nitrogen from the soil.  They also break down very slowly which is fine around shrubs and perennials.  In a vegetable garden where the soil is worked frequently, this isn’t ideal.  I’d suggest a layer of brown paper (like cut up leaf bags) covered with a layer of straw.  The paper and straw will control weeds and prevent moisture loss but rot away so it can be turned under to add beneficial organic matter to the soil.