Can I ship a MacBook in for depot repair?

Yes you can.

For Apple, a "depot repair" is an older term for a service option where, rather than repairing in-store, Apple opts to service the device in one of their centralized repair centers or "depots."

They don't use the term depot much any more, but the Send in for Repair option is the same thing. That is an option you will be offered when you use the web site to set up a repair.

Mac Repair & Service - Apple Support

Specifically, this option:

I did the mail-on/ship-in option for battery service for an iPad. As soo as I get when I got the confirmation from Apple, I took the device to a local UPS retail store. They already had the authorization from Apple and did all the packaging. By the time I got home I had a second confirmation that the device was in this system.

That was a Friday morning and Apple got the device Monday morning.. I had the iPad back before lunch Wednesday. Slick.

I don't know what you mean by "depot". To me a depot is a train station.

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