As far as I know Airplay is only 16-bits, but it's possible that it's the receiving device that is the limitation rather than the signal itself. For instance, the 1st Generation AppleTVs could output 16/44 clean. This meant that if you extracted a DTS Music CD to iTunes in Lossless or WAV or AIFF that AppleTV could receive the DTS music intact and output it to the receiver and the DTS signal would be present and work as expected. If you try the same thing with a 2nd or 3rd generation AppleTV that is iOS based, it will only output the signal at 16/48 and that destroys the DTS signal (and according to some audio purists is not acceptable to them for audio playback). But I know Airplay is still sending the signal intact because if I used a 2nd Gen ATV to play a DTS file but tell it to output to my first gen AppleTV instead of its own outputs, the signal arrives intact to that unit. So clearly, the Airplay signal is not the reason it's outputting 16/48 instead of 16/44.
So then the question becomes whether Airplay itself is limited in that regard or not and it's harder to tell because my testing of 1st Gen AppleTV hardware using XBMC instead and just regular SMB or NFS to transfer the files results in 16-bit audio output regardless according to my receiver (the frequency can change, though) so that tells me the AppleTV hardware itself or one of its drivers is the limitation (The first gen is running on an OS X Tiger variant so it's pretty old, relatively speaking). I have seen a DTS encoded demo file somehow convey 24-bit to my receiver, though in XBMC on AppleTV hardware, but someone else did the encoding (i.e. to encode audio files yourself in DTS requires their commercial encoder) so I can't say how they did it and I think it only ran in XBMC, not the AppleTV interface itself. To me, it's not a viable option either way since I can't encode DTS myself.
I realize I haven't really answered your question since your scenario involves a receiver and it's not clear to me whether the AppleTV hardware was the limitation or the Airplay signal when I used Apple Lossless encoding. But someone I know has an Airplay receiver by Yamaha and it has a bug in it its implementation that puts "clicks" and other sounds in the audio sometimes. I guess it was a known Airplay bug from a couple of years ago and Apple fixed it in the next release. The problem is that many companies never released an update to their receiver firmware to fix it so while this person doesn't notice it, I do and use her AppleTV instead to listen to music on that same receiver since that glitch drives me nuts (I've tried updating her firmware but they fixed other things, not updated the Airplay code). One would "assume" that newer receivers don't have that issue, but who knows, I'm just letting you know about her problem so you can be cautious either way.