It depends on the way in which the company classifies him as an employee ( i.e. contract, seasonal, temporary, etc.) , and the amount of hours he worked in the last calendar year, as to if he is eligible.
My guess is that, as an intern, he was not making more than $15 an hour. Unemployment will only pay half of that. Servers make more than that, most far more. No, it isn't a career position, but it will pay bills. It will also allow him to research and interview during the day.
As an employer and potential boss, it would show me A LOT to see a young person not sit back and compound our unemployment problems, while looking for what would amount to an entry level job.