No, they really don't. They do, however, indicate how many runs your offense is putting on the board when you pitch.
If you really want to indicate whether a pitcher is good at battling under adversity, the best possible way to do so is to divide their WPA (which shows how they affect their team's win expectancy per play) by their pLI (which shows how often they're being used in high-leverage situations), which gives you their clutch score. The pitchers with clutch scores over 0.0 (league average) tend to be the best in adverse situations that year - but even then, clutch scores tend to be random over a player's career.