Well, after some retraining, I have established the following facts concerning the Melee Training skill:
1- Specialization levels count for the bonus damage (I tested up to 8+2).
2- Specialization levels do not count for the % to cleave, however...
3- Specialization levels "trigger" the level 3 effect of having a % to cleave, for example, if you have 2 levels of Melee Training +1 with specialization, you can cleave, but only at a 10% chance.
I wonder if the skill is programmed like this on purpose.