I wouldn't do it.
Much of what makes a good licensed aircraft engineer is experience. Most LAMEs will tell you that you don't know an aircraft until you have worked on it for years as training course instruction and the real world can often differ.
This experience is best gained when young and super keen. As this experience is gained on night shifts in rain being filthy. Just knowing where a component is and what it does isn't enough, knowing how to change it out quickly, efficiently and combined with good trouble shooting is where you earn your way.
I agree with JamesA, Why would you want to take a backwards step after doing your degree, LAME/AME are these days are a much maligned group by management types due to what we cost. In my company new engineers are paid less ,different conditions etc etc (not sure if this is world wide) So you are a second class citizen in a group of second class citizens.
The above comment does not reflect my view on my profession for I am proud of what I do, it was more of an observation of how the industry is changing and what to to expect if you come join in.
Good luck but these days i don't recommend my job to any kids looking for a career due to the lack of career path...you could be working 12 hour shifts from the day you start till the day you retire/die.....