How does Airplay transfer audio file format to an Airport Express?

Yes. The AirPort Express Base Station (AX) works only with iTunes v4.6+ and is limited to music files that iTunes can read; ie, 16-bit data only. These data, though, can be in any file format that iTunes recognizes, from lossy MP3s at the low-quality end of the spectrum to Apple Lossless and lossless AIFF or WAV files at the high end. It is also important to note that the AX functions only at a 44.1kHz sample rate. When you play 32kHz or 48kHz data, iTunes sample-rate-converts the data in real time before sending it to the AX.

iTunes uses a QuickTime CODEC to convert audio files to Apple Lossless, and then, uses AirPlay to send them to the AX. In turn, the AX uses built-in software that converts the Apple Lossless to an Encoded Digital Audio format. From there, digital audio is sent to a optical transceiver to convert the electrical signal to an optical one before sending it to the innermost part of the audio port. For analog, the AX has a built-in DAC to convert the Encoded Digital Audio to Analog which is sent to the same audio port.

If so, would it still make sense for me to have AIFF files on my music server

or should I have ALAC files instead?