Yep, that's a copy protection measure. The game doesn't run if you haven't put the CD into the drive. There are games that allow installing the entire content of the CD to the HD, but this one, apparently, doesn't.
Yeah, if you have make a disc image of the CD and then mount it on your desktop, it will act just as if the CD was in the drive. I used Civ 3 that way.
I've found that all (all the ones I've tried anyway) OS X games will work if you make a disk image - under OS X they apparently don't get access to the low-level CD drive, so all they can do is check for a mount in /Volumes - but if it's in Classic then it'll want the actual CD. IIRC, AoE has to run in classic..