A very novel suggestion. 
My main issue with using Discourse this way would simply be expense …
Setting up a personal Discourse in the cloud and making it a private instance would, imho, be the way to go as this would ensure stability, easy upgradability and you could do all the nice back-up in the cloud things.
But that is not a super cheap option as you are going to have to pay for all the usual self-hosting costs although it’s not going to send many emails which will save you a bunch!
You could leverage an existing Domain though, and stick it on a special subdomain:
notes.mydomain.com
But then again, benefits:
- always available in the cloud on all your devices, both desktop and mobile.
- the experience of running your own instance (if you don’t do so already) and that it would be a very rewarding and potentially educational experience.