When you connect your ledger with metmask and eveything is working fine (cold wallet)
Is it still possible to use it without the ledger to another computer (hot wallet) when you install again.
This is more when you need to use the metamask urgent for some payments in case Ledger give you problems
If you import an address associated with your Ledger to your MetaMask wallet, that address will no longer be considered “cold storage,” because it is then immediately accessible from your MetaMask wallet. If you simply use your MetaMask wallet as an interface to your Ledger (i.e. the Ledger wallet is still needed to access the address and the address is not imported) then it will still be considered “cold storage.”
As you mentioned, yes importing a Ledger address will allow you to have immediate access to the tokens associated with that address.