If I am not mistaken the original problem was with a map control, so probably engine. But be careful if you have any other references to the featureclass in your code too because they will be just as hosed.
As for doing it in ArcMap, I wouldn't recommend it unless you have a compelling reason (I had to do it for a file workspace because ArcMap would cache the csv file schema and wouldn't refresh even if the layer was removed, updated (with new fields) and re-added.) I find ArcMap becomes somewhat unstable if it runs for more than a few days (some times a lot less) so I find shutdown as part of the workflow beneficial.