The source for not making a brachah on non-kosher or stolen food would be the Drashah on Tehillim 10:3, ".... and the robber congratulates himself for having blasphemed Hashem."
Shulchan Aruch O.C. 196:1 deals with this and says we are not to make a blessing on forbidden food in the beginning or after eating, (even a Rabbinical prohibition) even if it was an accident.
This strict opinion follows the Rambam; who learns it from the Mishnah in Berachos 7, that says we do not do the mitzvah of inviting (zimmun) on forbidden food. However the Raavad and Rosh seem to hold differently, The Raavad specifically says on the Rambam, that it may be that "zimmun" is not done, but why shouldn't there be a brachah? After all, the person benefited? Does the Raavad (simply reading his wording) mean to allow all blessings even if the violation was intentional?
The Taz interprets (as understood by the Mishnah Berurah) that the proper thing to do is to follow the Raavad by allowing the after-brachah in the case of an accidental violation. But, the Shaarei Teshuvah brings the Bach that seems to hold an after blessing is always in order. Furthermore, he brings that there was an authority that allowed someone who ate a food in violation of a vow to make the after blessing. But neither case allowed a blessing in the beginning of eating. Of course others disagree. The Kaf HaChaim (attributing to other authorities like the Magen Avraham) wants to say that in certain cases of theft the violator would be obligated to recite Birkat HaMazon (while contritely repenting) so as not to add the sin of eating without thanking Hashem (D'oraisa) upon his first sin of theft! He even says that the initial blessing may be recited by uttering it in his heart without actually saying the blessing. and the S.A. and its commentaries bring other related cases and opinions that are interesting and shed more light; but I feel it would be too lengthy and not directly addressing the scope of the OP. Suffice this for background.
However, does the OP's case of eating milk without waiting the customary time after eating meat, qualify as a blessing that would be "blaspheming Hashem" under Tehillim 10:3 and S.A. O.C. 196???
The Rema brings in Shulchan Aruch , Yoreh Deah, 89:1 that there are valid opinions who do not require waiting any time after one eats meat at all provided they finish the meat meal, make an after brachah and clean their mouth.
This implies that someone who eats dairy right after eating meat cannot be put into the category of a "sinner", even though R' Yosef Caro writes that you need to wait 6 hours and even the Rema says the standard custom is 1 hour (as well as saying he agrees that 6 hours is the correct thing to do).
So, it would seem the brachah recited on the "pre-mature" milk meal is not cancelled or wasted/rejected in any way. This is even true regarding someone who has a family or community custom (and such custom may even be Halachically binding; therefore I am in no way making less of a minhag) to wait a certain time and has violated it; since this custom is not universally accepted as actual mandatory Talmudic Law. In other words, it doesn't seem to be a clearly and universally forbidden D'Rabbanan act under S.A. O.C. 196:1 .
We can draw support for this lenient position in allowing both the first blessing and after blessing (even when the eater has not waited the proper time to eat milk after meat) even in the case of "mezid" (intentional violation) by relying on the Kaf HaChaim 196:1(7) in the name of R' Akiva Eiger.
S.A. Y.D. 97 says there is a Rabbinical prohibition to bake bread with milk, (and it is forbidden to eat that bread) because maybe someone will come to easily eat it with meat. (unless we make a small amount or give it an identifying shape or mark so it won't become confused) The same rules apply to bread baked with fat of meat.
Rabbi Akiva Eiger (although some argue against him) says that such a Rabbinical prohibition would not be strong enough to qualify as restricting the blessings upon anyone who eats the bread in violation of YD 97. (The bread is essentially kosher on all levels, were it not for the Rabbinical fence of what it could lead to.)
Therefore, when viewing the violation of merely waiting time in between milk and meat, which is only a Halachic custom, and not an actual prohibition upon the milk food eaten but merely eating it at the wrong time, there is certainly grounds to obligate the blessing before the meal and after the meal under all circumstances; especially Birkas HaMazon, which is a mitzvah D'oraisa (if you ate enough to be satisfied/full; and a mitzvah D'Rabbanan if you ate an olive's size or more).
Of course we should always strive to act in a way that everything we do is free of any questionable wrongdoing, and as always if you have a specific case, CYLOR.
Hope this helps. :)