Anonymous participant 626 incorrect, the regulations on the DLT website state that you must be in possession of a Non Immigrant Visa in order to apply for a 5 year license. You were lucky that your local office isn’t enforcing national rules.
People have done exactly that without issue. But, equally people’s applications have been denied for leaving the country. Some Embassies require an affirmation that you remain in country until the visa is processed.