If you develop an xAPI course package and don't yet have an LRS, or the LRS is down, then the student should not see any error messages. It will depend on the authoring tool you use. To be sure, you should test it.

We've gotten more questions about Articulate tools, so we're testing them preemptively, ourselves. So far, for Articulate Rise and Storyline, xAPI courses show no error messages if the LRS were missing. In Storyline, when you Publish, in the Reporting and Tracking Options for an LRS, you can turn off the “Report to an external LRS” option, and no data will appear in the LRS. Even with a trigger that sends custom xAPI, the lack of an LRS has no visible effect on the experience of a student.