In theory, this should work - but the most common problem is that different wallets use different derivation paths, which then does not automatically generate the identical wallet (private keys) you want to recover. Specifically as far as the Atomic wallet is concerned, I found this answer to a similar question :
That is correct, your XRP and EOS addresses have to be activated in the wallet. As Atomic produces your new unique addresses for every coin.
Our 12-word mnemonic seed is compatible with any wallet supporting 12-word mnemonic phrase. The way your assets will be transferred from Atomic is determined by the wallet you are importing your keys/phrase to
This means that they do not support the classic seed/private keys import, but only the sweep option.
I have some Tethers in the MetaMask wallet and it need Ethereum for swapping. How Atomic Wallet converts my Tethers automatically?