If you want to get into HVAC and sustainable design - good CAD skills/knowledge are a must (IMO).
While you have an engineering degree, unless you have experience with laying out the systems and such, there will be CAD proficient designers with no engineering degree who will still have sufficient HVAC engineering knowledge (layout and fitting and can do ordinary calculations) and will be able to put it on to a piece of paper as well. So you would be behind the eight ball starting out.
I would most definitely learn Cadd. But I would be leary of direct Autodesk assistance - they tend to not have industry specific instructors who can help you with HVAC issues. They will be able to teach you how to get into it, navigate the software, i.e. open files, saving, drawing lines, etc. - but when you ask them how to draw a duct or a pipe and use some of AMEP inherent design features, they will not be able to tell you how to do it. I know this from experience. If you want to go that route, find an Autodesk certified training company who works with the MEP industry. They tend to have actual designers who have experience in using AMEP in the consulting industry.
Also, you might look for a company that is willing to bring you on board as a designer (starting out) and give you the Autocad training free of charge and also help you learn how to use your ME degree in the industry. My company does that all the time and I am sure others do as well.