If my tooth decayed very deeply to the core, would i need a bone graft in order to get a partial denture applied on top?

Maybe: Bone grafts after extraction (socket preservation) will maintain more bone below the partial denture. You have to weigh the perceived advantages with the cost. Discuss with your DDS.

No: First the tooth must be extracted.Unless an unusually large amount of bone must be removed from the alveolar ridge in order to remove the tooth, your dentist can place a partial denture either immediately or after a healing period. Of course your remaining teeth would have to be healthy and capable of retaining the new partial. Consult with your dentist.