If there is no dc-removing capacitor in the circuitry , then should I
not expect that for a board using a single (positive) supply, that the
signal is always above zero?
No, you can put a negative voltage in, as long as it doesn't go below
-3.33V. You need to look at the schematics -- the 8132 is a
differential opamp with a common mode output set at 3.3V/2.
Basically, the differential amps will clip if you go outside the range
of -3.3V to +3.3V. You will also damage the differential amp if you go
below -3.3V.
The ADC will clip if you go outside the range -2V to +2V when set for
minimum gain.
Back to the subject of what your signal generator is doing, I don't
know. If you measure the voltage on the sma connector with nothing
connected, you will see that it is 0. If you connect a 1 V source
through a 50 ohm resistor, you will see that there is 0.5V at the
connector. If you connect -1 V through a 50 ohm resistor, you will see
-0.5V at the connector.