The gemara tells a story of a woman who complained that the Rabbononin the house of the Reish Gelusa were sitting in a stolen Succah. Rav Nachman ignored her complaint because although the wood that was used for the succah was stolen, by building it into a Succah, they acquired it through תקנת מריש and only need to return the value of what they stole. The point of the gemara is that for the duration of Succos we consider any material built into a Succah to be as if it were built into a permanent structure like a house. Just as the Rabbonon made a תקנת השבים to say that a beam that was built into a house doesn't have to be disassembled and returned, they made the same takana by a Succah for the duration of Succos (but if the owner is willing to wait until after Succos and wants his wood back, then it must be returned).
The Takanas Marish is essentially a d'rabonon method of allowing the thief to acquire what was stolen without having to go through the technicalities of yiush and shinuy. If the wood would have actually undergone yiush and a shinuy ma'aseh or shinuy reshus, there would be a kinyan on it without any special takana d'rabonon, but the chiddush here is that although there is no technical kinyan, the person is koneh based on this takana and doesn't need to return the beam. It would seem that just as when one makes a kiyan d'oraysa based on yiush and shinuy, they can still not make a bracha on the succah (as tosafos 30a points out - שאני ברכה דאיכא נמי הזכרה לשם שמים).
However, the Mishna Berura (637:15) writes that based on the takanas marish one can even make a bracha. In the Sha'ar Hatziyun (21) - דבודאי ריש גלותא ורבנן היו מברכין עליה גם כן, he indicates that the source is that the Rabbonon who were sitting in this Succah would not have sat in a Succah that they couldn't make a bracha on, therefore they were presumably making brachos. This seems to be a big chiddush. Simply, the takanas marish itself is a chiddush in that it applies to succah, and it would seem that it should be as good as a kinyan d'oraysa, not better than a kinyan d'oraysa. The M.B. seems to understand that the takanas marish is more powerful than a kinyan doraysa of yiush and shinuy because it enables you to even make a bracha.
It seems to me that this issue is contingent on what the Rabbonon did with their תקנת מריש. Did they merely institute that it doesn't need to be returned once its used in a Succah just as if it were used in a house, but the heter for the mitzvah haba'ah b'aveira is the standard approach that whenever one is koneh prior to the mitzvah, it is not a problem of mitzvah haba'ah b'aveira. Based on this approach it should be exactly like the halacha when there is yiush and shinuy, one can be yotzei but NOT make a bracha. Or did the Rabbonon make a special takana to address the mitzvah ha'ba'ah b'aveira, meaning that they pretended as if there were never any beam stolen, just that the value is owed to the original owner. Based on this approach, it is as if there was no aveira done with the beam so that one can even make a bracha on the Succah.
It seems to me that this is contingent on a machlokes between the Ritvah and Tosafos in Gittin. The Ritvah writes הרי העצים האלו שסיכך בהם קנויים לו מדרבנן מתקנת מריש, ואין עליו אלא חוב דמיהם שחייב לבעלים, והרי הוא כחוב דעלמא ומשלך קרינא ביה, וליכא נמי משום מצוה הבאה בעבירה, דהא קנינהו מקמי מצוה. The Ritva seems to hold that the way around the mitzvah haba'ah b'aveira is that you are koneh the beam prior to the mitzvah, therefore the din should be the same as whenever you are koneh prior to the mitzvah that you can't make a bracha. However, Tosafos in Gittin 55a (d.h. mai) writes ובסוכה לא בעינן משלכם, ולא מפסלא אלא מפני מצוה הבאה בעבירה, וכי קניא בתקנתא דרבנן לא חשיב מצוה הבאה בעבירה. It is very meduyak from Tosafos at the end that only by the challah case where the right to use it was that he was koneh before the mitzvah are we machmir not to make a bracha, but not when the Rabbonon institute to view it as if there is no aveira done. Tosafos seems to hold that the way around the mitzvah haba'ah b'aveira is that the Rabbonon make a takana as if it were never stolen at all, therefore this should work to allow even the making of a bracha, as the M.B. paskens.