Using AppleCare before it runs out I have a first generation Apple Watch Sport with some minor cosmetic imperfections and scratches after two years of use, with Apple Care+.
The support runs out soon, and I was wondering what use it the cover has. 

Specifically: If I were to 'accidentally' 'drop' my Watch, could I claim that on Apple Care and get a brand new one, or at least screen?
The hardware accidental damage coverage is only good for 2 incidents over the life of the AppleCare+.  Each incident is subject to a US$69 service fee + tax.  

You don't have to accidentally drop your Watch, you can just tell them that the glass was accidentally damaged during normal use and you want to make a claim (assuming you haven't already made at least 2 damage claims so far).  You'll be charged a service fee and they'll either repair the glass or provide you with a refurb Sport watch.

There should be no need for moral quandaries while doing this.  You bought the coverage to help you for this very purpose.