I would imagine so, in all honesty.
As you said not wishing an injury on him, but if Lebron James has just finished his 13th season in the NBA at the age of 31, moving on to 32.
His career path has been eerily similar to that of KG up to this point...
* Lebron (like KG) came straight from high school to the NBA
* Lebron (like KG) was 19 years old during his first NBA season
* Lebron (like KG) played his 13th NBA season at the age of 31
* By the end of his 13th season Lebron has played in 987 regular season games out of a possible 1,066 and averaged 38.98 MPG over those 13 seasons. KG by the end of his 13th season had played 998 NBA games out of a possible 1,066 and averaged 37.94 MPG over those 13 seasons.
* By the end of his 13th season Lebron has played in 199 playoff games at an average of 42.13 MPG. KG by the end of his 13th season had played 73 playoff games at an average of 40.96 MPG.
* Lebron has played in 12 All-Star games, while KG (by the end of his 13th season) had played in 11 All-Star games.
* Lebron so far (over 13 NBA seasons) has been very durable - he's played in 92.5% of possible regular season games and has played < 69 games in a season only once. KG was also incredibly durable during his first 13 NBA seasons - he had played in 93.6% of possible games and had only 1 season in which he played less then 71 games.
After his 13th season his body started to break down.
Over his final 8 seasons KG has managed only 464 games played out of a possible 656 (an average only 58 games played per season, or 70.7% attendance) and he averaged only only 27.06 MPG over that stretch.
KG took great care of his body his entire career and was incredibly durable, but at the end of the day he put a LOT of mileage on that 250 pound body of his, and his very physical style of play didn't help.
Lebron has been similarly durable so far, but he has put a similar amount of mileage on his own 250 pound frame, and plays a very physical game - it's only a matter of time (IMHO) before his body starts to break down from sheer wear and tear.
Off the top of my head I believe Kobe (who also entered the NBA from high school) also started to see his body breaking down around that same time in his career.
KG was lucky that he was such a good midrange shooter, and that probably helped a LOT to prolong his career by reducing some punishment on his body in his later years. The same could be said about Kobe. Lebron has never been a good outside shooter, so unless he makes some dramatic strides in that area, I can't see his body lasting any longer then KG's did.