The repeat is nearly immediate – so way faster than the autorepeat. but it’s not instant, so it doesn’t happen on every keypress.
An additional note, this mainly (only?) happens when I access the server via a VPN connection into the company – when I access the server inside the company’s LAN, it doesn’t happen. but parallel ssh connections through the VPN, or Lync voice calls, etc, don’t show any anomalies in regards to connectivity.