Yes, patients with periodontitis can have dental implants fitted, but only once their periodontitis has been treated and brought under control first. Otherwise, there is a strong chance that the patient will suffer from periimplantitis.
Even once their periodontitis has been brought under control, patients who have had periodontitis are more likely to develop periimplantitis than patients who have not. Therefore, before extracting a tooth we must always be sure that said tooth cannot be left in place with appropriate treatment and maintenance.