Can my device, which was enrolled with ADE, receive MDM profiles if there is no internet connection during initial setup?

No. All Apple devices must connect to the Internet to complete initial enrollment. As part of the initial power on process, the devices must reach out to Apple's activation server to determine activation type. This requires internet access. The flow on both macOS and iOS is Language, Country, Accessibility, Network. Failure to connect to a network will prevent you from completing device activation. The activation server will determine if the device is associated to an Apple Business/School Manager tenant. The device is then directed to communicate with the assigned MDM. This displays the Enrollment window during Setup Assistant.

After enrollment and initial profile delivery, all devices must connect to the internet to receive additional or modified payloads. This is because the delivery of profiles if triggered by push notification. An internet connection is required for push to function.

Hope this is helpful. You need Internet to enroll and manage devices.

Yes, but an internet connection will be required at some point to retrieve the configuration. The configurations won't be there initially and it will require manual work to get them on the device.

*This only applies to macOS devices. iOS, iPadOS, and tvOS devices must be set up with an internet connection. Also, beginning with macOS Sonoma, macOS devices may need an internet connection for setup as well.

Confirm the device is enrolled in Apple Business/School Manager.

Confirm the device is assigned to the MDM.

Confirm the MDM is set up for ADE.

Then on the macOS device, while logged in as a user with administrator privileges, open Terminal.

In terminal, enter the following command:

sudo profiles renew -type enrollment

and then hit enter.

You will be asked for the password for the admin account. When you type it, it will look like nothing is happening. This is normal behavior. Type it anyway and hit enter.

You may or may not see a popup in the top right corner asking you to enroll in device management. If you don't see it, it may be hidden in the Notification Center.

Click this alert.

This will open system preferences/settings and ask if you want to enroll.

Choose Allow.

You should see the MDM profile and any scoped profiles begin to install on your device.