Yes, in theory it is possible to prevent these kinds of infections without resorting to secure boot (e.g., by insisting that all the suppliers of components of the motherboard start designing components that cannot be pwned) but so far all the computers you have actually been able to buy that are immune to these kinds of infections achieve that immunity with secure-boot technology.
It seems to me that, in this situation, secure boot’s only role is to provide a false sense of security, which could make recovery from the attack less likely.
In contrast, verified boot might somewhat mitigate the damage from being able to use the BMC to write arbitrary data to the SPI flash chip. Emphasis on might — at best I expect that it would require an attacker to be a bit more creative in how they design their exploit payload.
Secure boot can include the hash of the firmware, computed by the root-of-trust that can't be tampered with by this attack. So the exploit will make the keys stored in the TPM inaccessible.
This will make the tampering conspicuous, at least.