Issue summary:
You are trying to upgrade the VM insights VM Insights Linux dependency agent and want to know if it would cause a server restart.
Recommended solution:
As per my understanding, server restart is not required for dependency agent upgrades.
You can upgrade the dependency agent manually or automatically using the following methods available and described here:
We would also recommend to have automatic extension upgrade enabled. You must ensure the property enableAutomaticUpgrade is set to true and added to the extension template. This property must be enabled on every VM or VM scale set individually as described here:
https://learn.microsoft.com/en-us/azure/virtual-machines/extensions/agent-dependency-windows#automatic-extension-upgrade