I am wondering if there are any potential issues in moving large Outlook PST files (e.g. a few 3–5GB Outlook files) into Dropbox?
The files are periodically accessed / altered and might increase marginally in size.
Per the Dropbox help centre, Dropbox doesn't sync files that are in use, so your PST files probably wouldn't sync in real-time. They would only sync when the user closes Outlook. However, when it does sync it will only do a differential copy (only the changes to the file are copied), so it won't have to re-upload the entire file every time.