Is there a way to get the distance estimate between an iOS device and a beacon WITHOUT having the 1-meter calibration value saved on the iOS device beforehand?
YES, you simply read the CLBeacon accuracy field as you suspected. This is an estimate of the distance to the beacon in meters.
This estimate uses an undocumented calculation that is based on the RSSI measurements (likely a 30 second running average, perhaps discarding outliers) combined with the 1-meter RSSI calibration value embedded in the iBeacon advertisement. A port of this calculation to Android is shown here.
And, no, there is no way to read the calibration value from an app. It is obscured by iOS, which disallows seeing the details of iBeacon Bluetooth LE advertisements. See here for a detailed explanation.