Michelle,
It sounds like you are talking about the publishing option on a File, not an Assignments. The reason for that option is to prevent students from access that file unless there is link to it from somewhere else, such as an assignment, an announcement, a quiz, etc. One that reasons I use that option at times is if I'm adding an image to a test question and I only want students to have access to that image through the actual quiz.
So to answer your question, if you are making an Assignment in Canvas and link to a file that is set to "only available to students with link", they will have access to the file when they click on the link in the assignment.
Rick
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