Should a professor recommending me talk about my (bad) grades in his or her letter?
It really depends on how the professor knows you.

If the professor only knew you "after the change", the letter might say "I am aware of student's relatively low grades during the first few years, but by the time of my class, they were a top-performing student", that kind of thing.  

If the professor has known you for years, it might be appropriate to comment on having observed this change, and expressing confidence that you can handle the role in question despite the low cumulative QPA.