If I have my DAW (Ableton) blocked from accessing the internet via Microsoft firewall, and I run my DAW as admin. Will my DAW be able to bypass the rules I set up, that prevents it from any inbound and outbound connections to the internet?

 

The change or blocking in the firewall only affects the internet, so you're preventing
Ableton from communicating with the outside world via the internet.

Imagine it like a house you live in with a front door, and the front door is now closed.
A rule you've set in the firewall is permanent and can't be overridden.