Yes, having active untreated periodontal disease is an internationally well known risk factor for the infection spreading to dental implants placed in the same mouth.
Both peri-implant mucositis and peri-implantitis are characterized by an inflammatory reaction in the tissues surrounding a dental implant that can lead to tissue destruction and ultimately, implant failure. Peri-implant mucositis is confined to the soft tissue with no sign of supporting bone loss. Peri-implantitis, similar to periodontitis, results in inflammation around the soft tissue as well as progressive bone loss. Additionally, peri-implant mucositis may be successfully treated using nonsurgical efforts if detected early, whereas periimplantitis usually requires surgical treatment.
Recent reports revealed that peri-implant mucositis was present in 48 percent of implants followed from 9 to 14 years after placement. However, because peri-implant mucositis is reversible with early intervention, it is quite possible that its prevalence could be under-reported. Research concerning peri-implantitis reported distinct differences in the incidence and prevalence from numerous authors with studies ranging from 6.61 percent disease prevalence over a 9-14 year period to 36.6 percent with a mean of 8.4 years after loading.
According to Paul Rosen, DMD, MS, Chair of the AA P Task Force on Peri-implantitis, "Although there are widespread clinical reports where dental implants have achieved long-term success, it is important for dental professionals to understand that peri-implant mucositis or peri-implantitis may arise from a failure to identify risk factors, improper treatment planning, suboptimal surgical or prosthetic execution, and/or improper maintenance care. We can't ignore the reality that patients could be suffering from peri-implant mucositis or peri-implantitis and should continually work towards understanding the disease, treatment and contributing risk factors."