[Suicide Junkie]

The goal of a reactor would be to absorb all of the gamma rays for use by ship's systems. None need be emitted by the ship.

The thermodynamic argument is simple. If the cloaking device prevents the ship from emitting energy (in order to be undetectable), then the ship can't be losing energy.
Since the ship is generating energy to power lifesupport, the cloak, and anything else they're using, the energy in the ship is monotonically increasing.
At some point, the temperature of the ship will exceed the melting point of its hull, and its bye-bye cloaked ship.

Thusly, the ship must be emitting at least as much energy as it is generating, averaged over time. Even when cloaked.
This can be in the form of neutrinos, large numbers of low energy photons, small numbers of high energy photons, hot particles, whatever.
It is highly unlikely that you would see gamma rays. That would mean that their reactor is not powering the ship, and is unshielded (in the lead-wall sense).