If the O2 sensor is allowing the engine to run rich, it will shorten the life of the convertor. By how much, I can't say, but I wouldn't let the condition go very long.

2002 X5 3.0 324,600 miles
2014 428i 28,000 miles

2004 325i sold at 123,600 miles
2001 325i sold at 66,000 miles

1970 Firebird - Under restoration