I think the only "dense" thing here is Dan.

... on the remaining distance to the bugged satellite. All the way to Jupiter, there's a very noticeable inverse-square law at work ...

It's not that you need incredible amounts of electric energy to get your signal to punch through, though. However, the amount needed usually is greatly reduced by the use of very directional, very large antenna assemblies. Which brings us right back to "inconspicuous" ... not to mention that the authorities, who might still be sending stuff to the fleet, can afford to make for a way stronger signal, drowning out the wannabes.

A lot of it depends on the Fleet's tech and processing power to separate every radio signal, no matter how weak, unscramble them from each other and analyse each one for interesting data.

It's true the military can send a much stronger and focused signal which would (and did) undoubtedly get the fleet's attention over the noise, but they would have to be doing that over the broad spectrum of radio waves if they intended to somehow block or distort other signals from getting to the fleet. Its true that you can reduce the necessary power with directional antenna, but the necessary power is all about keeping the signal readable to the receiver over the noise. A big part of them is actually the receiver rather than the transmitter, to focus on signals from one direction and ignore or remove the noise signals from others to get better range on reading a specific signal from a specific direction without others garbling it. For the fleet, this is a difficult task since the Earth isn't much more than a pin [EXPUNGED] of light from Jupiter to begin with. in a perfectly quiet environment, the signal will travel and be legible almost indefinitely. With natural cosmic background it's still fairly realistic that a mere satellite phone signal could reach the fleet in a legible state, particularly since they can easily filter that out with a focused receiver pointed at Earth.

I recall a rover sent to Mars which was supposed to send signals back to Earth through a satellite in Mars orbit, but when the satellite failed to work they were still able to pickup the rover's attempted signals to the satellite.

The problem is that Earth has billions of signals being transmitted across the spectrum which all garble each other after a distance, which brings us back to the question of just how good the Fleet's tech is at still deciphering the signals after that significant distance and flagging Gharr's transmission in all of it. So the stronger (and/or more focused) the signal they send, the better the chances are that the fleet can both receive it and mark it of importance from among the many others. But for all we know, Fleet tech is capable of even picking up satellite phone signals legibly... Dan and Gharr are probably just unaware of the fleet's capabilities... or Dan is still an idiot and is just going for a super powerful signal without considering how powerful he really needs the signal to be.

Might be that they help each other. Dan seems overly pessimistic but Gharr is noted as an eternal optimist. Dan's pessimism, particularly to humanity in general, is certainly beyond healthy standars... But Gharr's optimism got crew members killed and generally dumped them into this mess. All because he dismissed the more cautious and pessimistic approach of Zane and lied to him about humanity's level of advancement to make the risks seem negligible.