I converted VHD to VHDX with Windows Server 2008 inside on a test machine and it successfully booted.
Inside VM itself I didn't notice any fails or errors after conversion.
As far as I know an OS inside a VM and a VM itself do not care about virtual disk type so it is not related to a guest OS.
At the same time Windows Server 2008 hypervisor doesn't give an option to create a VHDX so it is not related to a host OS.
Just out of curiosity what "This format is not supported in operating systems earlier than Windows Server 2012." is related to?