No,
But Typically most players will not dye a head with mesh still on it for two reasons.
1. Wear and tear on your stick will cause that mesh to fade so for example if you dyed it black over time the mesh will turn gray or a light black.
2. Some times if the sting/mesh is to tight with the head you will not get a correct die and some parts of your head will be the original color and others will be the color you dyed it.
So the answer to your question no it will not mess it up but i would suggest that you buy colored mesh and dye the head separately to avoid these problems.
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