A central hub of Azure cloud migration services and tools to discover, assess, and migrate workloads to the cloud.
As per MS article (https://docs.azure.cn/en-us/migrate/concepts-assessment-calculation), it looks like migration discovery shows that this OS is ready to move to azure. you may get more visibility pnce you have the discovery project created.
If azure migrate is not supported, you still can move this machine by converting vmdk into vhd (looks for tools which covert. there may be free or paid tools). after conversion upload the vhd into azure using azure storage explorer and then create VM.
OS support:
The machine windows 2012 would run without any issues in azure.. And I dont think you would receive patches(azure update manager may not supported, but manually patching done if needed).