It seems that also 10th Karmapa was a layman, he was wearing a long hair and was traveling in a company of many women (this was noted by the 5th Dalailama, when the two of them met), so I doubt that he was a bikshu. Tibetan histories tend to "monasticize" teachers who were actually not monks at all, or they were monastics only for some earlier part of their life - for example Longchenpa. Also Milarepa is being presented as celibate (though not monastic) by some teachers these days, while the early biographies are said to speak of Milarepa having multiple consorts.
In Tibet there seems to be a sentiment of looking down on the practitioners who have given back their vows and continued as a laymen no matter how high capacity this practitioner could have - Shakya Shri is one of several such practitioners. So I think this is also reason for covering up a history of nonmonastic teachers in a monastic lineage. Several Shamarpas were clearly laymen, yet they are depicted as monastics in the lineage paintings of Karma Kagyu.
Probably a good idea to separate ordinary lay practitioners from enlightened masters (who were not ordained), because such beings were in every sense identical to monks (apart from their clothing). Conventional divisions like non-monastic versus monastic and celibate versus non-celibate are therefore not really applicable.
In the 16 Karmapas, Karma Thinley Rinpoche records that the 10th Karmapa was ordained at the age of 21 at Tsurphu. He spent most of his life in exile due to his association with the Tsang chieftans who were in conflict with Sera and Drepung. He returned to Tibet once in that time to seek out the Shamar incarnation, and he disguised himself as a layman. It is very interesting that the 5th Dalai Lama records he was dressed as a layman. Perhaps after 30 years, he had become accustomed to this lifestyle. There is no suggestion he gave up his vows.
There isn't any evidence to suggest Milarepa maintained the Brahmacharya, this is made up. He is said to have taken Tseringma and her sisters as consorts, but I think it is also fair to say his activity is completely inconceivable.