Lost macbook, but it was never registered to my account

The short answer is: "no".

The longer answer is: You don't "register" Apple devices at all. If she didn't sign into her Apple account on the device and activate find my, it can't be located, tracked, locked, marked as lost, or erased.

Not sure what kind of "claim" you intend to file. I would not expect an airline or airport to compensate you for something you forgot on a plane.

If the airline doesn't have it in their lost and found somewhere, it's gone.

Check your homeowners or renters insurance to see if they might cover it.

Please read If your Mac is lost or stolen - Apple Support. It exhaustively describes all possible solutions.

The plane went on to many locations so its hard to know which airport to even file a claim with.

Due to various required (•) security inspections, the Mac was most likely discovered on her flight and removed from that aircraft prior to its subsequent departure. Contact the airline, tell them the flight number, date, destination etc and ask for their local "baggage service office". Use that terminology. Things whose owners cannot be found wind up there... for a while, after which they will be disposed of at the airline's discretion.

• All this assumes it was a US Part 121 scheduled carrier.

You can't add a device to an account remotely. It gets added when the Apple Account is logged in to iCloud and Find My is turned on.

You say she set it up, but not registered it. Not sure what that means, there is no registration process.

If she said it up, then it usually she would have logged into to her Apple Account for iCloud and enabled Find My at that point.

If she did not log in to iCloud or did not enable Find My, then there is absolutely no way to track the Mac short of magic.

If she skipped the step to enable Find My, then there's no way to track it anymore.

That's the point of the step, to enable tracking

It cannot be added to an account remotely and then enable Find My remotely, it must be done directly on the device.

Sorry.