I would like to know, will the existing estimote sdk (1.4.0) detects the beacons when the app is in the background / killed? If Yes, will the detection works in all versions of Android?
or should i switch to, Proximity SDK for this?
You should switch to Proximity SDK for this. Androids starting from 6.0 have more and more restrictive background services that makes BLE scanning less responsive. See https://developer.android.com/about/versions/oreo/background.html.
In Proximity SDK you can run scanning in low power mode or run it as foreground service (requires notification).