It is very difficult to comment on the OEM board, i dont know if the bios from Intel site will work for the OEM board. And i dont know the consequences.
One thing i am sure is that you are correct in thinking that a bios update may be needed to support the lga775 cpus. Sometimes, it does not only depends on the bios, there are other factors which need to be considered.
For example referring to our Intel (R) Board D102GGC2:
There is a list of supported CPUs
As a reference, you can check the release notes for the latest bios for the intel board d102ggc2
You will see that there has not been any update mentioning that new cpu support have been added.
Hopefully someone else can help you further on this.
All the best,