Some little tidbits to add to the discussion...
1) M4A is a container, and multiple audio compressions use it, mainly Apple Lossless (aka ALAC which is lossless) or AAC (which is lossy).
2) Honestly, I'd just ignore bitrates (or what you're calling bps, Paul) if I were you guys. Not only are bitrates not really an indication of quality or if a file is lossless (or not), because of the compression used bitrates of FLAC files will almost always have lower bitrate numbers than uncompressed files. In addition, there are types of music (e.g. solo piano pieces) that compress pretty darn well, and will have lower bitrates than you'd think they should have (which might make you question quality) but it's entirely normal. Also what makes bitrates irrelevant (IMO) is when you're playing compressed files they're automatically uncompressed to PCM and that's what you're hearing when playing them back. You won't notice a difference or hear any differences if a compressed FLAC file has a lower bitrate number versus a uncompressed AIFF file. If you're thinking a lower bitrate means lower quality, you're thinking of MP3s (and lossy formats in general) which is certainly true for them, not for FLAC (or any other type of lossless) files.
3) Compressed FLAC and AIFF files are both lossless. If you convert 1 compressed FLAC file to uncompressed AIFF, the data between both are 1:1. When you play both back, the device decompresses the compressed FLAC file when playing it back, so it's still 1:1 with the original source (of course, if it's ripped correctly if it's the case of CDs).
I found out that telling the converter to make the files 24kHz wa making the files larger than the original AIFF which defeats the object.
Do you mean 24-bit? If so, that's bit-depth, which a completely different thing. If you're converting 16-bit files to 24-bit or 24-bit files to 16-bit, you're actually dithering files which isn't a lossless conversion (nor is resampling). I'd avoid doing that if the original files (e.g. files ripped from a CD) aren't 24-bit to begin with. Not only are you doing a lossy conversion when dithering files from a ripped CD to 24-bit, you're also wasting hard drive space.
Just to be certain I understood, m4a files, ALAC, are lossless just like FLAC?
Look what I said above, M4A is a container which multiple compressions can use. M4A files can be either Apple Lossless (which is lossless) or AAC (which is lossy).