Wipe before upgrading from stock nexus to CM? Since CM is based on stock Android (AOSP), and the Nexus 7 is a stock device, can I just flash the CM zip without first doing a wipe/factory reset?

I just wonder if it's possible to avoid the hassle of backing up and restoring all my apps and settings, widgets, email settings, etc...
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? :)