No.
The Management Server is primarily the control plane. A running VM is actually executing on the hypervisor host.
So you should distinguish between:
Management Plane
→ CloudStack Management Server
Compute Plane
→ KVM / other hypervisor hosts
A Management Server outage doesn’t automatically mean that every running VM stops.
However, management operations such as provisioning, configuration changes, and other CloudStack API/UI operations can be affected.
This is one reason production CloudStack environments may use multiple Management Servers.