We do not yet know. Gigabyte specifically says ECC memory is compatible, but runs without ECC on their boards. Asrock only says that ECC ram is compatible.

I asked Asrock support earlier this week:

  MSI and Gigabyte explicitly mention "(operate in non-ECC mode)". 
  Is that also true for Asrock AM4 motherboards? Or do they fully support ECC?

Reply:

  From: ASRock Support <snip>
  Date: Mon, Feb 27, 2017 at 10:17 AM
  Hello,
  ASRock AM4 motherboards fully support ECC function.

Still, someone will have to test to be sure.

It does. Asrock support claims their AM4 motherboards support it.

ECC support is a motherboard feature, not a CPU feature, isn't it?

It requires that the memory controller support ECC and that there are extra traces from the memory controller to the RAM.

This used to mean it was solely a motherboard feature, but starting about a decade ago, the memory controller was moved onto the CPU, so now it requires both CPU and motherboard support.

Actually it's depend on both motherboard and CPU.