Currently the Bitcoin Core client, v0.15.1 (64-bit) on macOS Sierra 10.12.6 still go in App Nap mode after being hidden behind other applications or docked in the macOS dock bar. Keeping the app in foreground will obviously avoid the App Nap mode. At the moment it is even impossible to disable per-app Nap Mode via the Get Info dialog because there is no option to do that with the Bitcoin client app.
The App Nap issue was already addressed and solved in few previous ticket (#3182, #5041, #5804).
I don't really know how App Nap can interfere with the client performance, at the moment i'm syncing the whole blockchain and it's taking a lot.

