Yes, the B2 will play m4a files.
M4A is a file extension for an audio file encoded with advanced audio coding (AAC) which is a lossy compression. M4A was generally intended as the successor to MP3, which had not been originally designed for audio only but was layer III in an MPEG 1 or 2 video files. M4A stands for MPEG 4 Audio.
Both M4A and MP3 file extensions are used for audio-only files. Audio-only MPEG 4 container files usually have an M4A file extension. M4A files are unprotected. Protected files usually have an M4P file extension.
AAC or M4A file quality is better and file sizes smaller compared to MP3 files. M4A files sound better than MP3 files when encoded at the same bit rate due to some of the enhancements made to the format such as:
Programs that open M4A files include iTunes, Quicktime, Windows Media Player, and Roxio Popcorn, Toast and Creator. Some media players will only play the format when renamed to MP4.