Can I use my 128GB macbook air to temporarily run a 512GB / 1TB back-up?

I was thinking what I would do if my macbook pro with 512gb storage failed, the technical service delays would certainly disrupt my workflow severely

I have a macbook air that I use seldomly, in addition to my main macbook pro (the macbook air is my previous macbook)

Is it possible to:

1. Connect a >512GB external HDD to the macbook air


2. Restore the time machine backup to the macbook air's external hdd


3. Use the macbook air for a while


4. Get another time machine backup from the temporary external hdd setup


5. Restore the time machine backup of (4) to the macbook pro when it arrives from the technical service - therefore restoring the original functionality/setup

The steps (2) and (5) are the issue here, as I haven't done any macos restore's and don't know about the process