Wipe before upgrading from stock nexus to CM?
What you are describing is what's known as a "dirty flash" which is a no-no! Especially from AOSP to CM and vice-versa, could lead all sorts of force closes etc. Likewise, [a particular custom ROM (insert of your choice)] to another but different [custom ROM (insert of your choice)] and vice-versa. 

The only time a dirty flash can be performed if going from CM nightly to the latest nightly, or [custom ROM] to a more recent version of same [custom ROM], theoretically, although no guarantees that everything will work "proper". Occasionally force-closes will be exhibited or some "weirdness" will manifest, hence no guarantees. 

Really, if going from one ROM to another - best to wipe cache/data completely provided a backup has been done in the first place :)

Why not use a backup tool such as Titanium Backup or the basic backup tools found on the Play store in the event you are not rooted? :)