You do need Google Play, or a suitable replacement, because most android apps won't work without it.
F-Droid apps do not need Google Play Services. OSMand (offline maps) and other apps works without it. Telegram probably should work too, but I did not test.
AI also says that it is possible to have push notifications without Google.
alt Hacker News
F-Droid apps do not need Google Play Services. OSMand (offline maps) and other apps works without it. Telegram probably should work too, but I did not test.
AI also says that it is possible to have push notifications without Google.