Yes, if you have the permission to search for Non-Students, you can navigate to the page of the user whose Student List you’d like to see if you click on the caret next to the user's Assigned Students for the Term.
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A saved search is a saved set of parameters. Each time you run a saved search, it will return the set of students who currently meet those parameters. For example, if you create a saved search for Freshmen, the list of students who return for that saved search a year later will be different than at the time of its creation, as many of the freshmen will no longer be in that classification. A Student List, on the other hand, is a static list of students, saved by their student ID, and the list of students will remain the same over time.
This shouldn't have any impact. The Student List, like any Advanced Search filters used, is only initially relevant for helping query the list of students you want to be a part of the campaign. Once they have been added to the campaign how they were added (category, list, filter) does not matter so changes to Student Lists would not impact campaigns that have already been built/executed.