Anything is possible, but it isn't really to clear to me what they are requesting and I would want to ask a few questions about this arrangement which would guide you on how this would be compensated. In general, Medicare only covers services that are considered 'medically necessary', which means are for the diagnosis and treatment of an illness or injury. So it would not be an issue to evaluate and order tests for patients who have some symptom or condition that would make such a service necessary. But for the patients who are not symptomatic, why is the doctor seeing them and what would the doctor be doing? If there has been an outbreak in the facility and exposure has been suspected, that could be covered, but if not, this could be considered a screening or preventive service, which may not be covered. Also, is the doctor actually testing the patients or just collecting specimens? Or just checking them to see if the test is necessary and then if so, ordering it to be done by an outside lab?
As long as the services provided are medically necessary and covered, it should not be an issue for your provider to see the patients and bill for this, but if that is questionable, you may want to look into an arrangement directly with the facility or with the patients individually rather than trying to bill Medicare separately for each service.