My dad has a feeding tube and is having trouble getting his pressure sores to heal. Are the two related?

Possibly. Adequate nutrition is essential to heal any kind of wound. That your father has a feeding tube implies that he needs more nutrition than he can get by feeding himself. That said, it is also essential to keep pressure off the pressure sore to promote healing. Some pressure sores are deep enough that they will never heal without a surgical procedure, but adequate nutrition is necessary to heal that.
Yes. Nutrition improves healing of ulcer - protein supplementation esp arginine, citrulline helps in addition give zinc, vit c, multivitamin, vitamin k2.
Distantly. The feeding tube implies some form of nutrional support is needed [for many possible different reasons]. The pressure sores will not heal or improve if his nutrition is poor.