Core does not update your wallet. Once you choose a hard drive, it will sync the blockchain and you will be able to access the wallet stored in this directory.
But updates or backups to the wallet file itself are not done.
That's the point though. The
entire folder is his "backup".
OP now has Bitcoin Core running on Windows box, fully synced, with a wallet.dat...
and a full copy of the Bitcoin Core datadir (including blocks, chainstate and wallet.dat) in his external drive that can be connected to the Ubuntu netbook.
Personally, I think it's slightly overkill to have a full backup of the blockchain... But if you have the storage and bandwidth, why not?
The only issue I can see with this setup... Is the potential for things to go wrong if OP wants to encrypt the wallet.dat and/or changes the wallet passphrase. Doing either of these things can cause problems as then the wallets will be using different seeds/addresses.
OP would need to ensure they then copy the wallet.dat with new passphrase from one system to the other. You cannot simply changing the passphrase on the 2nd wallet.dat as that will create a new seed/addresses for that wallet.dat and there is potential for coin loss.