No. Sepsis meaning infection in the blood can occur in any surgical patient; and certainly immunosuppressed transplant recipients, but it is not common. It can derive from tubes, drains, IV sites, the lungs, or other infected organs, etc. It is reported in 1-5% of transplant patients.
Increased risk. Patients who have undergone a solid organ transplant typically are taking immunosuppressive medications to prevent rejection of the transplanted organ. Generally speaking, this immunosuppression places patients who have undergone a transplant at higher risk of acquiring sepsis.