Yes, so long as the grad placement is a contract rather than a permanent hire. The placement would be full-time hours. Hatch would be the employer-of-record for the duration of the placement.
If the grad is successful, you can convert them to a permanent position at no cost. At that point, you would become the employer-of-record.
Students must have access to their university email address
The one thing that has to be true is that the student can still verify their student status. Verification is tied to their university email address, so anyone who still has access to that email can verify, including recent grads.
That means Hatch Students is the best fit for students still studying and about to graduate, or students who have recently graduated and still have access to their email.