I looked on the HCL located here VMware Compatibility Guide: System Search and could not find your motherboard. That being said, the best way to test would be to download ESXi and see if it installs successfully. You may have to roll some drivers into a custom install ISO but since Gigabyte uses fairly standard components, it will probably work with only a lack of RAID and possibly a non-functioning NIC. You can get Intel gigabit NICs for $20 or so and be working just fine.
Your motherboard uses a Realtek Gbe adpater. If you search that on your favorite search engine with the "esxi driver" in the search field, you will find a lot of resources. I don't like to post links to external sites that I don't own and I'm also pretty sure it might be against the community rules to do so.