Yes, crepe batter can be made ahead of time. In fact, resting crepe batter in the refrigerator for at least 30 minutes, or even overnight, is often recommended for improved texture.
Making crepe batter ahead of time offers several advantages. First, it allows the gluten in the flour to relax. When flour is mixed with liquid, gluten develops, which can make crepes tough if cooked immediately. Resting the batter allows the gluten strands to relax, resulting in more tender crepes. Second, resting allows the flour to fully absorb the liquid, creating a smoother batter and preventing lumps. Finally, it gives the bubbles formed during mixing a chance to dissipate, which also contributes to a smoother crepe. To make crepe batter ahead of time, simply prepare the batter according to your recipe, cover it tightly with plastic wrap (pressing the wrap directly onto the surface of the batter to prevent a skin from forming), and refrigerate for at least 30 minutes, or up to 48 hours. Before cooking, whisk the batter gently to recombine, as some settling may occur. If the batter seems too thick after resting, add a tablespoon or two of milk to reach the desired consistency.
If you're short on time, you can still rest the batter for a shorter period, even just 15-20 minutes, to see some improvement in texture. Avoid over-mixing the batter, as this will develop the gluten further and counteract the benefits of resting.