Yes, if you have Internet access, it's possible via Google Maps Geolocation API and information about nearest mobile operator cell or/and wifi access points
You need send requests like:
https://www.googleapis.com/geolocation/v1/geolocate?key=YOUR_API_KEY
with information about target Cell Tower (how to get LAC and CID you can find here) or WiFi access point in request, and if target WiFi access point is in Google database your got response JSON with Lat/Lon and accuracy.
NB! But sometimes it returns completely wrong results.
For show current position you need to disable "standard" MyLocation tool
googleMap.setMyLocationEnabled(false);
and use custom, like described here.