Provided I create a Private DNS zone on GCP attached to a VPC, will this cause any issues on existing workloads currently running on the VPC? Do I need to allocate time for downtime?
A Virtual Private Cloud (VPC) network is a virtual version of a physical network, implemented inside of Google's production network, using Andromeda.
Private DNS zones are part of Google Cloud DNS which lets you publish your zones and records in its DNS without the burden of managing your own DNS servers and software. Updating DNS records within a Private DNS zone should not require longer periods of propagation time unlike Public DNS zones.
Both of these features/resources are managed by Google Cloud Platform's own production network and DNS. These are different from resources that you manually provision with limited spec, so creating a Private DNS zone and associating it to an existing VPC running with workloads should not affect its performance or cause downtime.