Two weeks ago ( Nov 1 ), the Check Engine and VSC cluster of lights came on for my '05 4R LTD V8. Scan tool indicated catalyst (first one from exhaust manifold) in Bank 1 efficiency "Low", hence DTC P0420. Up and downstream O2 sensors read "OK".
Back in mid Sept this year, the alternator crapped out about 4 miles from home and Limp Mode came on. Made it back to house at a crawl pace with frequent "minor explosions" ( ? ) from the exhaust system. At that time I thought those ME's were from excess gas igniting in the cats as I had the throttle pegged to the floor to get it moving at the crawl pace speed.

My questions:
1. Is the present DTC a result of this excess fuel dirtying the cat's media and is there a cure ( e.g. a bottle of cleaning fluid ) that will resuscitate the cat. If so, please provide suggest product data. Or, I'm SOL and cat replacement is the only solution.
2. Will operating the vehicle w/the DTC do permanent damage. Vehicle is use only for short ( 10 miles) round trips into town for groceries.

Any recommendations, advice or real life experiences are welcome

If it's the downstream sensor (hard to tell from your post) then it has absolutely no control over fuel economy, emissions, or engine safety. Their only purpose is to throw a CEL when the system thinks the cats are not operating fully. The upstream sensors actually matter because they're what controls air/fuel ratios.

I just put an o2 sensor spacer on my downstream sensors when I had this issue but depending on emissions inspections in your area that may or may not be a viable option.

Sounds like your alternator crapping out caused the coils to misfire and raw gas dumped into the exhaust which can be bad for cats. I think short trips as well if they're never getting up in temp to fire off. My wood stove has catalytic convertors and it's very important to keep your temps up or they can be harmed.

Continuing misfires associated with unburned fuel definitely kill cats so maybe your severe, short duration experience could have done it in. I am doubtful that cat cleaning snake oil does any long term good but people try it when they have to pass emissions testing. No problem continuing to drive with a bad cat. Also, I don't believe the downstream O2 sensor controls anything - it just serves to detect a malfunctioning cat and lighting your CEL.

I would take it on a long highway drive, about an hours worth and see if that "self cleans" the cat. As stated, cats like to be hot to function at their best.

Much thanks to all with your inputs, really appreciated and did lessen my stress level to use the vehicle or drive it for any distance.

For the record, I did replace the downstream O2 sensor after getting the DTC. The upstream O2 sensor on this bank ( # 1 ) was replaced 15k miles ago. Other than the lights being on in the dash, the 4R runs great as before. Now knowing that engine will not suffer any lasting damage from a bad cat, I'm going to take a few long drives as suggested to heat up the cat(s) and hopefully that will be the cure.

Luckily, I do not have any annual emmission checks to worry about here in Ontario.
Thanks again for all the help.

Hi everyone,
here's the update to my DTC P0420 problem.
I searched the web for O2 sensor extenders ( also called spark plug extenders ) and had more positive user results than negative. Also came across some who had dump a bottle of Seafoam into a full tank of gas and again with mixed results ( best case from the Seafoam additive was lights went off for 2 years but came back ). Decided to try the O2 extenders ( @Cezar . Thanks ) and installed a 90 degree extender to the downstream sensor. Almost two months now and the lights have not returned. For good measure I threw a full can of Seafoam when tank was at the half full mark. Fingers & toes crossed.
Thanks again everyone.

Can vouch for the o2 extenders working. I have them on mine to get rid of p0420 and p0430 after installing my headers. Have also used them on other cars for cat efficiency codes. They work.