Well, I need a little more information to give you really sound comments, but I will speak in generalities for now. Extractions after radiation treatments can be dangerous because the bone around the tooth extraction site doesn't always heal properly. Radiation causes hypovascularization, and with this diminished blood and oxygen supply, it just doesn't behave the same any longer. The condition that becomes a problem is called osteoradionecrosis. It involves an area that just will not heal properly, and this can become a major problem. How much risk this involves is usually dependent on the total amount of radiation exposure, and the amount of time out from the actual treatments. The longer the better, but after a certain point it really doesn't improve any more. The healing process can be augmented by saturating a person with oxygen prior to the surgery and during the healing in a pressure chamber like those used to treat SCUBA divers for the bends, except they increase the amount of O2 in the breathing mixture. It can take from 20 to 40 "dives" in a chamber to get the desired effect.
Most likely what the doctor is referring to is a titanium dental implant. These are a proven treatment in normal people with success rates in the high 90% range. Success in radiated patients is not as good. The titanium post becomes osteointegrated right into the bone permanently, and a false tooth made from porcelain over a metal understructure can be cemented or screwed to the top of it.
Re: the area of darkened radiolucency on the x-ray. This indicates an area where the bone has died back, or where an abscess might exist at the tip of a root. If it is an abscess (I cannot tell you this from what you have told me) the safest treatment plan would be to not do an extraction and implant, but to do a conventional root canal treatment, combined with antibiotic treatment for the associated infection. This eliminates messing with bone that is already compromised, and may not heal properly. If it is an area of dead bone, then it is likely that the tooth would have to be taken out. Your reference to the root itself being gone, is confusing, since there are few things that would cause the destruction of the root itself, especially after it had been there for so long.
Before the surgeon decides to extract the tooth, be sure that he is completely aware of the radiation treatments, understands the consequenses possible, has a contingency plan if healing becomes and issue, and that the possibility that this is not just an abscess which could be treated with antibiotics and a root canal has been eliminated from the differential diagnosis.
Lastly, you know that I think the people at MD Anderson walk on water, and calling them for an opinion before you leap wouldn't hurt anything. I can give you the name of someone there, who I trust implicitly, but I prefer not to post Dr's names in the forum. Let me know if you want it by email.