Not really. He, in a crueler trick of fate than the third blow, died just before recording became commonplace. However, he did record some Welte-Mignon piano rolls. These have been out for a while, but their importance is undiminished. If you want to understand both the approach of the greatest conductor of his generation and how Mahler approached Mahler's music, then you must get this disc.
The two big surprises are how fleet his tempi were and how he approached the architecture of the music. Compared to Reiner, Levine, and the rest of the major interpreters of the 4th, Mahler positively sizzles through the score. I am not sure how many sopranos could keep up with an orchestra playing at what seems like Mahler's prefer tempo. However, on an internet message board discussing this record, I suggested that Mahler might have been speeding things up because it was a piano roll. To my mind, there could be some issues with ensemble cohesion if you took the finale at Mahlerian speed. However, it is illuminating to see how Mahler conceived of the piece.
His approach to the architecture of his own work, and, according to the oral history "Remembering Mahler," the work of others, was novel. Rather than deal with music in terms of measure or bar, he shaped tempo and dynamics on the phrase. In fact, it seems like he would all but stop the sound between the phrases to emphasize his approach. Only Wilhelm Furtwängler had an almost identical approach. John Barbirolli also seemed to deal with music, particularly Mahler, in a similar manner. In the opening bass 16ths of the Second, Barbirolli stops the band between runs in his June 1965 Berlin performance. Mahler does almost the same thing during the Trauermarsch transcription. Now, granted, there might be rests there - I don't have the scores in front of me, but there is a clear full stop. However, Furtwängler and Mahler seemed to have been on the same wavelength. Hearing how Mahler conducted, a loose, rhythmic style, one sees Furtwängler.
These are important records of the greatest composer and conductor of the late 19th Century and early 20th. They answer many, many questions that all serious Mahlerians have about Mahler and his style.