OK, first of all, we need to clarify what is meant by "radio". Sounds stupid, but the unit in the dash that has all of the radio controls on it isn't the actual radio unit. This is what Saab calls the Infotainment Control Unit (ICM). The actual radio is behind the dash, out of sight. All of the audio components are connected together on a fiber-optic network called the o-bus. If there's a break anywhere on the o-bus, no radio functions will work, and the turn signal sound, key chime, and warning sounds won't work either. If this is the case with your car, you need to find the break.
By far the most common cause is the amplifier that's mounted under the driver's seat. To be sure, have a competent Saab tech check it to determine the problem, as audio components can be pretty pricey for these cars, and it's worth a small diagnostic fee to be sure.
The car will run if any one of the audio components is disconnected, but I'm not 100% sure about the ICM. Not a lot of trouble with these, though, so that shouldn't be an issue.
I've never seen an aftermarket radio in these cars, probably due to the optical network I described above, so I can't comment on that.
It is possible to by-pass the radio, amp, etc, if the o-bus is by-passed also. Again, a Saab tech could do this fairly easily.
If any of this isn't clear, please feel free to write back. Thanks for checking in with us!