I have one bar at home, just did the speed test: 16Mb down, 6Mb up. If you dial *#0011# you'll see your RSRP exactly (reference signal receiving power), mine shows about -105.
If calibration was done properly it should be something like this:
0 bar - 0- 20%
1 bar 20-40
2 bar 40-60
3 bar 60-80
4 bar 80-100%
So even at 0 bars you could have OK reception.
But there is more to it, you can have strong signal, but also strong interference and a lot of other users could jam up otherwise strong connection.
To be honest I'd much rather have zero bars and still connecting, than phone lying to me that I have good signal and not able to connect.