Hello tlhp,
Thanks for checking in for advice on this before letting your client proceed. Following the correct procedure when migrating from QuickBooks Desktop to QuickBooks Online will make things move much more smoothly and reduce the chance of running into any problems. Let me explain.
You're correct in saying that the migration needs to be complete before your client can start using their QuickBooks Online subscription. They have 60 days from their QBO sign-up date to migrate their data, and after that date they'll need to start a new subscription. Once the data is migrated, they'll be able to get started with invoicing and using QuickBooks Online Payroll, otherwise, as you said, the data will be overwritten.
Here's a great article that goes over the migration process from start to finish. It'll be a great reference and will ensure that you are completing the process correctly: Migrating from QuickBooks Desktop to QuickBooks Online.
Let me know if you have further questions or concerns. I'm happy to point you in the right direction.