If you want, you could shoot both sports without ever classifying. In USPSA, you are allowed to compete as "Unclassified" forever, though if you shoot many matches you will shoot enough classifiers that you will eventually become classified. If you are not a USPSA member, you will never have a classification, as classifier scores of non-members are not maintained.
IDPA requires that you reclassify annually, in the sense that if you mean to shoot a sanctioned match (state, regional, or national championship), you must have shot a classifier, for the division in which you intend to compete in the sanctioned match, within a year prior to the match date. If you shoot only local club matches, you could probably continue to shoot without classifying. All clubs are required to run at least one classifier match a year, so again, unless you are trying to avoid becoming classified, you will be able to do so without trouble.
To answer your question; you can shoot whatever division you want, whenever you want, and it doesn't matter if you are classified in any division, let alone the division in which you are competing.