No, writing down your 24 recovery words is optional.
Your microSD card wallet backup already contains the same information.
However, some people prefer to write down their recovery words as that's what they're used to or punch them into metal for additional protection against disasters.
An additional advantage of having a wallet backup written down is that you do not need to use the backup recovery tool if you ever need to restore your wallet backup on a non-BitBox02 hardware wallet. If you only have the microSD card digital backup, you would first need to use the backup recovery tool in order to obtain the 24-word mnemonic seed from your microSD card backup.