Can CD's be loud and ok?

The latest Steely Dan release is mixed loud, but it sounds quite good. The audible distortion you hear on some records is because at some point in the recording process they exceeded digital zero. Sometimes this is done by accident, and though it's hard to believe, sometimes it's done on purpose. To call an engineer's use of compression distortion is to miss it's creative uses. Virtually all of your classic (60's - 80's) rock has used compression as a creative device. Check out the Kinks "All Day & All of the Night". One of the reasons alot of professionals love recording to analog tape is the gentle compression effect it gives. Vinyl mastering also has some well known compression artifacts.

The direct answer to your second question is yes, it's possible, but such a recording might not have the best signal to noise ratio. You won't be able to get the slammin' in your face sound of recent pop/rock recordings without the use of advanced compression techniques, but your recording can still be reasonably loud.

The dynamic range of live music is enormous and dosen't easily translate to any recorded medium. Limiting and compression are automated volume regulation techniques used to control the wide dynamic range signal. Using a compressor is the equivalent of turning up the volume when the sound is soft and turning down the volume when the sound is loud. Originally the performance of the compressor was supposed to be imperceptible to a listener, but then came the British Invasion. Several artists used audible, aggressive compression as an integral part of their "sound". The modern use of "hyper" compression is the result of artists emulating the sound of loud radio stations. There's nothing inherently wrong with the use of compression, but like any effect, it's over use can be annoying.