Now that we are using the feature that triggers an SCCM SUP sync when new 3rd party updates are published, we have turned off the schedule for running the SCCM SUP sync since we want to sync everything, including Microsoft updates, after running the PatchMy PC sync. Currently, if there are no 3rd party updates that sync/publish, it won't trigger a SCCM SUP sync to sync all of the Microsoft updates that might have released. Having the option (Check box) to always trigger vs. only when a 3rd party is actually published would be helpful.
We wouldn't recommend turning off your native sync schedule within SCCM. If you schedule your SUP sync for an hour or two of our sync time it should have plenty of the time to publish our updates before the native SCCM SUP sync.