No, financial institutions (FIs), direct reporting NFFEs, and branches that are limited will not be issued GIINs. This is explicitly stated in the IRS FAQ from 2023, which clarifies that limited FIs, direct reporting NFFEs, and branches will not receive GIINs. Additionally, the transitional period for limited FFI and limited branch statuses has expired, and such classifications have been removed as FATCA classifications, further supporting that limited entities are not eligible for GIINs.
Sources:
Publication 5188 (7/2020)
Instructions for Form 8957 (06/2018)
Publication 5118 (07/2021)
Instructions for Form 8966 (2023)
Publication 5190 (2/2022)