Hey joeflint,
The VDS upgrade does not involve downtime from any version. There were some issues when upgrading to VDS 6.6 as you can see here: VMware Knowledge Base . However VMware recommends to do a backup of the configuration from the vSphere Client in case something goes wrong.
Try to do this upgrade when there are not a lot of tasks running and personal recommendation is to change DRS to manual before doing this to avoid vMotions starting while you are doing the upgrade. However, "upgrade" is only one click.
And remember, before upgrading the VDS, all your ESXi who consume that VDS MUST be version 7.