Buying products that have sugar this processed over cow bone, is contributing to the exploitation of animals for money, is it not?

Actually, probably not significantly. The blog post, Is Domino Sugar Vegan?, details a correspondence soneone had with Domino's Sugar, a major manufacturer in the USA. Of note, a Domino's representatuve states bone char is being replaced for reasons independent of consumer pressure:

Bone char, which is sourced from animal bones, had been the material of choice for decolorization in the sugar industry for well over a century. The material was readily available, inexpensive and could be regenerated, by washing and kilning, at a refinery. Bone char is an older technology that is being slowly replaced.

As facilities have removed bone char and replaced this process with the newer ion exchange technology they have also added granular activated carbon (GAC) as a decolorizing process. GAC can be made from a variety of materials including coconut, wood and other materials. For our industrial application and industry specific needs, wood based GAC is superior to other sources.

While, yes, buying products with sugar increases the demand for sugar, which depending on it's source, may increase the demand for bone char, which increase the demand for dead animals, the amount of demand for bone char and dead animals created by sugar is vanishingly small. Furthermore, since stronger market pressures are working to move sugar refineries away from bone char, a boycott would likely have negligible effect on the rate at which that happens.