The 6XX would probably improve with a good desktop DAC/AMP. Generally Bluetooth isn't as good as wired(though there are excellent wireless implementations out there), so there's that.
Even with lossy formats you'll likely still notice the uptick in quality. 192 AAC is listenable, you could maybe notice its weaknesses with good gear, but it will be decent (compared to, say, a 128 MP3...). Either way, it's better than FM Radio!
I think it's worth it for the 6XX, to experience why they're so special, but I certainly don't think it's required. That said, you shouldn't need to spend a large amount to get something good, which is the crux of audiophilia typically.
If you could upgrade your library to FLAC/ALAC you'd probably be doing yourself a service.