Yes, you could. It will all depend on what you're aiming for. Perhaps you want the most little geometry as possible and you are saving poly's wherever you can. Or maybe you can afford more geometry for a better detailed model and so you can go and add more polygons so your model can be more high definition. Sometimes it can be a workflow limitation, other times you can go crazy and add much more. So it'll all depends. Also it will depend if it's for games and then it'll depend on the engine. So like always in Blender, it depends. But don't be afraid to do it your way, mostly there's no right or wrong, just the approach you decide to take.
Short answer is, in this case, mostly no. Beveling would add additional detail for the UV Map and texturing, but it wouldn't necessarily make the edge sharper looking. Also with that angle you would probably have to play with the bevel's profile to get the proper look. This is of course looking at it from a game development aspect. For 3D VFX and animation then beveling would most likely be the preferred method.
Mark Sharp has a few things that it can be used for that bevel can't. There are modifiers that use it to reduce or ignore those edges for processing. It also affect shade smooth normal calculation and the newer geonode modifier(auto smooth/shade by angle) doesn't export to most outside texturing tools or game engines.
You will find that when it comes to 3D there is a lot of it depends. To use the CG Cookies mindset the answer would be try it out. Play with both. See how they differ and make lots of mistakes. As Wayne says, "Making mistakes means you're learning." I'm paraphrasing but the lesson is still the same.
Jumping in here to confirm what has already been mentioned, but as was said already: you absolutely could have beveled that edge instead. Whether you sharpen the edge or bevel ultimately will come down to personal preference or intended outcome/use-case.
Is this wand intended to be viewed up close? Are you going to see the silhouette profile of that edge? In that case, you may want to add a few beveled loops to it. Otherwise, you can save some polygons by simply marking it as sharp and relying on the baked normal map to convey the idea that is it more rounded than it actually is!
As the classic saying goes: It depends. Your mileage may vary but it could be a great learning experience to see if there even is a difference between baking out a normal map from an edge that is sharp vs. a beveled edge!