Wright's just been lucky, a tool I used to use a lot on THT is called PrOPS. It adjusts OPS based on LD, GB, etc. and home park. It's a bit like tRA in a way that it uses those events, but much less accurate since hitters have more control over their BABIP than pitchers. PrOPS has Wright at .766, suggesting that he's been lucky. Since Wright's usually a high BABIP guy, you could probably safely add .100 or so points to that OPS (as his BABIP is usually about .50 higher than average, so .50 to OBP and .50 to SLG). But, in comparison, Wright last year was at .956.
But to answer the question, Wright's HR drop will likely just affect his batting average, not BABIP.