Is it possible for this device to transmit over radio, or only receive? I certainly prefer only being able to receive, as transmitting seems like an attack vector.

With the assumption that it only receives, I would strongly prefer that it be left on by default. Adding a second source to the CRC mixing can only improve entropy, even if the source is controlled by an attacker. Since the noise from the zener has no simple proof of it's entropy output rate, and it can vary over time, and because zener noise TRNGs have been known to be power-supply noise sensitive (not that your's is), having that second source gives me much more confidence in the device.