Thanks a lot, I didn't know about that dnsmasq feature.
I looked a bit about dnsmasq and NetworkManager, and it seems there is already some integration supported. The following page for Ubuntu shows some integration is in the works where indeed dnsmasq is used to handle DNS request routing: https://blueprints.launchpad.net/ubuntu/+spec/foundations...
With a bit of time (for upstreaming too as I use Debian) it looks as this will be handled out of the box. Nice!