Sorry to restart such a old thread but maybe someone in the future will have the same doubt. This is already possible, just:
start Bluestacks and enable Android Debug Bridge (ADB) in preferences
open a cmd
go to the folder you uncompress the android SDK and in platform-tools ex: C:\fpcupdeluxe\tools_r25.2.5-windows\platform-tools
run adb connect localhost:5555
thats it!
as log as you have running bluestacks when you create the APK it will connect to bluestacks, install the app and runit
also if you want to get the logcat just in the same CMD run
adb shell
the prompt should change to something like
OnePlus3T:/ $
there just type logcat -d
to view the logcat or
logcat -c
to clear it.