Hi @KendylNeill11,
I'm not sure what integration you have between Banner and Canvas, but I'll say in general issues like this are often best worked out among the campus offices (IT / registrar / admissions / enrollment / etc). At my institution, we don't allow faculty or staff to add students to a course manually at all, since that circumvents so many other university processes and procedures. If we have an issue where we think a student should be in a course and they are not, we go to our Registrar's office to find out what the issue might be and ask that it be prioritized if it's something on our end to the automated enrollment scripts get the student into Canvas ASAP. When we first implemented Canvas years ago, there were more occurrences like this, but they were really gaps and cracks in university processes that were causing the issue, and once those were identified and addressed, the issue basically went away. Not to say it's easy to do, but in the long run I think this is the best way to go. Manually adding students in works, but can cause all kinds of issues like the ones you mentioned when they finally do get their official enrollment. Manually adding also gives other offices who may "own" the broken processes a way out of not fixing things, as they could just say "well manually add the student, no big deal."
I hope this discussion helps a little even though it's not necessarily an "answer".
-Chris
-Chris