If all of the information needed to recreate your mnemonic seed phrase is stored digitally in an online computer, then you will be greatly increasing the attack surface for any potential hacker. There are ways you could store this digital data more securely, but ultimately having it stored in an online computer will ALWAYS be less secure than having a true 'cold wallet', whose keys/seed phrase have never existed on an online machine.
If you are just storing the hash of your seed phrase, then that would not be enough for an attacker to steal your coins. However, you will need to input your seed phrase into some device in order to run the hash function, so something simple like a keylogger could skim your seed phrase when you do so. You could run the hash function on a permanently offline machine, and then transfer the output value to an online machine for storage, but I'm not sure what the point of doing so would be. A hash of the seed phrase will not help you restore your wallet later, you'll need the seed phrase itself to do so.