He's asking about 2FA on his Apple ID, not other apps or services that are signed in on his phone.
The transition should be fine, but especially if he has other devices other than his phone on the same Apple ID.
My advice would be to make sure he has his recovery codes for Apple ID. Either print them out or have them available on a device that does not depend on Apple ID to sign in.
A recovery code is optional. However, if you choose to use that feature you can no longer use account recovery to reset your password - if you forget your password, lose the recovery code, and do not have access to a trusted device (from which you can reset your password) you're totally out of luck - there will be no way to regain access to the account.
As I see it, the recovery code is a way to prevent anyone else from trying to gain access to your account via account recovery. The problem is, it can also prevent you from regaining access to your own account. I wouldn't suggest using it unless you happen to be a person with a higher-than-normal need for security.
If I was using a recovery code not only would I keep them on a device that does not depend on Apple ID to sign in (as any device can potentially be lost or be otherwise unusable), but I would keep print-outs in at least two separate places - one could be on-premises, the other should be off-premises (bank safe deposit box, etc.). I'd also keep the number in a password-keeping app that stores data in the cloud so that the loss of an electronic device does not result in the loss of the recovery code.
Basically, I would keep that very important "egg" in multiple baskets, some high-tech, some no-tech.