No, the institutional business official is responsible for ensuring that investigators and personnel have appropriate visas. If NIAID issues a grant award and later finds out that a visa does not allow an investigator sufficient time to be productive on a project, NIH can take action which may include terminating the grant.
Read our Foreign Workers on NIH Awards SOP for additional details. Also, be aware that certain awards (e.g., most career development awards) list U.S. citizenship or permanent residency status as an eligibility requirement in Section III. Eligibility Information of the notice of funding opportunity.