Since about 38,000 miles, the engine light has come on about every 20,000 miles or so and diagnostics coded the catalytic converters as this issue. I believe dealer wanted about $1,800 to replace them, but technician indicated that the coding is not always correct on this and probably the only thing that would happen is the fuel efficiency and possibly emissions performance would be affected. Light has now come on permanently now. From what I can tell the gas mileage has not been affected much -- never got much more than 37 MPG on average and we are getting that now. Can I do damage to the engine by not replacing the converters?

Of course you can damage an engine. Its possible for the converters to clog so bad that it develops back pressure and that can harm rings and valves.

What Im really wondering is since this has been going on for so long that how come when it first started you didn't get it fixed under warranty as it is a smog related item ?