The question covers a wider issue than what you explicitly ask. To contact an author about a manuscript that you have not reviewed is not unethical as such but carries with it several other issues. You will essentially provide comments as any other colleague of the authors would except the comments would be unsolicited. If you contacted the authors as a reviewer outside of the review process the matter would be very different, of course.
First, there is the personal issue. How well do you know your former professor, do you think he/she will react positively to your comments "out of the blue"? I think it is worth thinking twice about providing comments on something the author would not expect you would necessarily see other than as a reviewer of course. If this happened to me and the colleague was a close friend with whom I feel comfortable discussing our respective science freely it would not be a problem. But, somewhere is a line where the comments would be come uncomfortable due to an uncertainty about the reaction.
Second, as an author, I would not expect the journal/conference to send out the entire article when asking for reviews. That behaviour is closer to unethical than what your question concerns. It is more appropriate to provide the title and abstract to the prospective reviewer so here I think the conference, in this case, should make their routines more strict. As you can see from this perspective, it is not your fault you have gained access to the entire manuscript so at least you are not, in my opinion, breaking any confidence, that has already been broken by "the conference".
So while I do not see any strictly ethical problems with providing comments, you should perhaps consider the action twice before continuing for the first reason above. I am sure there are differing opinion about this but the main problem here lies in the fact that you were given access to the entire manuscript even though you have not agreed to be a reviewer. In an open review system this would be perfectly fine but I would be quite irritated if I found my manuscript has been distributed to large numbers of prospective reviewers.