Is there any way I can see what students will see in my Blackboard course site?
When Edit Mode is off for a course, the view is similar to that of your students. The only exception is that you will see the Control Panel (and they don't) as well as an Edit Mode toggle button in the upper right-hand corner (that they don't see either). Anytime you want to preview a certain portion of your course to see it as your students see it, just click on that link in the course navigation menu.
However, disabling Edit Mode will not allow faculty to interact with all course activities exactly as a student would (for instance, taking a Test); for that, you will want to enable Student Preview.