Does playing harder defense result in more injuries?
That's an interesting question.
I found this on Twitter: (@mangameslostNBA):
NBA top 5, impact on teams by players lost to injury (Lost-vorp metric, lost value over replacement player)
1 GSW
2 PHI
3 NOP
4 LAL
5 BOS
Also this:

The top 5 teams in the league defensively:
MIL
UTA
IND
TOR
OKC
Boston is #6
From the info above, I'm not sure I see a clear correlation between the teams that play the best defense (which we can probably infer means trying harder on defense) and injuries.