I think Time synchronization is important, but Timezone is not.
From what I see EventQueue timestamps use UTC time, whatever the local time of the system, so long as the clocks are in sync they can all convert to Universal Time.
While do agree with @owen-niblock that mixed timezones can easily cause confusion when reviewing logs (as log timestamps are local time), and also cause confusion in custom code, I don't believe it would cause an issue with Sitecore operations.
However; if I had such a broad and distributed server setup I'd probably already have them all logging to a central log aggregator which consolidates the logs, makes them searchable, and normalizes the timing.