Is there any way I can tell if the NAS supplies the necessary real time notifications?
Yes, you can watch the scheduler on the Schedule tab sheet. It should show "Monitoring Folders" and as soon as you make a change directly on the NAS, the "Monitoring Folders" has to disappear and be replaced by a date + time a few seconds from now. You can compare the behavior against what happens when you make a change on the local hard drive.
If I need to force a sync sooner than an hour, can that be done easily?
Yes, in the Profile Overview, you can right-click on the profile and choose "Run in Background".
If I get rid of real time sync, is there anything else I need to do to insure that deletes still happen?
Just the settings that you already have (SmartTracking, Safety).