Should you snowshoe with Poles? Most definitely, but go out with Germans, Mexicans, and any and all other nationalities too! Should you snowshoe with “ski” poles? It really depends, but for most snowshoeing, I suggest leaving the poles at home.
Poles can certainly help with balance in very rugged terrain or loose/deep snow, be used a crutch to relieve stain on a weak or injured leg, help when using a heavy pack or pulling a sled, help provide some propulsion on steep uphills, can help you get up on your feet if you fall and they are useful in probing animal scat, thin ice, etc.
Studies have shown that using poles when you walk or run requires 16 to 23 percent more energy than going without. If you really want to burn more energy, work some on upper body development, normally walk or run on dry ground with poles or need help overcoming special situations, take poles.
The best poles to get if you choose to use them are the two or three section collapsible type whose length is adjustable to fit the snow depth and terrain conditions you require. What really make these poles valuable is that they can be made very short so they can be easily stowed in a pack for the vast majority of snowshoe conditions when you will not need them.
Perhaps many snowshoers think they need poles because they see skiers using them. Skis are narrow, somewhat unstable, slippery and possess little traction, so poles come in very handy. Snowshoes have the opposite attributes, so poles are much less useful.
Perhaps snowshoers think they need poles because the pole companies say so. Try snowshoeing without poles first before you decide that you need them.