Monitor existing radio traffic? Would work at least for bandwidth and drop rate, maybe not latency. If the user isn't using the radios, fall back on a signal-strength based estimate. For bonus points, learn the estimated connectivity based on correlations between previously measured radio metrics and signal strength in the same location.
Or just hide the bars and show a binary "go/no-go" symbol to indicate if the phone has a current radio connection. Your phone is always connected to GCM or Apple's equivalent so why not use the health of that connection as an indicator?
How would you run a test often enough to keep the signal information up-to-date, without impacting data usage and/or battery?
It's a great idea, but I think there's a reason we don't do it. RSSI values work well enough.