I run an Apple TV to an older Theta DAC while I save up for a BDA-1. I love it. It makes organizing and finding music very easy. Something that I thought I'd have no use for on it was YouTube. I've been watching a ton of live performances. Pic and sound quality varies, but its a ton of fun.
I chose it over the other streamers for a number of reasons - local hard drive eliminates drop outs, computer doesn't need to be on, can be controlled by an iPhone or iPod Touch, and its TV interface. The Apple TV's interface has changed recently. It now has an internet radio tuner.
In regards to Apple Lossless and compression, it doesn't sound compressed to my ears. There's no loss of dynamics, closed in sound, etc. as far as I can tell.
My DAC's optical input doesn't sound as good as its coax input. Its not a night and day difference, but there's a difference. My Apollo and Apple TV sound the same through the optical input. Both reported have a bit of jitter through their optical output.
The BDA-1 reclocks and reportedly rejects jitter extremely well, so I doubt there will be any issue.
Just my 2 cents.