RYP, time to join the reddit world... It's eating every other form of collaborative forum and link sharing upvote/downvote type site.
The main problem with satellite phones is that they were not designed to be stealthy RF-wise. When in use they're a fairly powerful localized transmitter on a fixed set of bands that are easy to identify on a spectrum analyzer looking at the 1350-1750MHz band. In addition the antennas on an Iridium 9555 or similar are not very directional. For those who've used one, you're familiar with how the users manual shows you how to bend the antenna's angle "up" if you hold it to your left ear. The antenna on the end of the stick is not properly directional with a very narrow beam width, it's actually covering 30 to 50 degrees of sky if you aim it "up". This is necessary because it's a constellation of low earth orbit satellites, the several satellites that might be above you at a given time are in constant motion during the course of a 5 minute phone call.
I do think it would be much harder to locate an Inmarsat iSatphone (from the ground) if it was paired with a highly directional dish shaped L-band antenna. One, because you can aim an iSatphone at a fixed point in space (it communicates with a single geostationary orbit satellite above your hemisphere, wherever you are, and is not seen as moving from a point of view on the ground). This would require some soldering and surgery to the iSatphone to remove the bar shaped antenna and wire it up to a 1 foot diameter parabolic reflector dish on a mount with an L-band feed. But this method would result in a great deal less spurious radiation spewed off to the side of your transmitter.
Any competent Ham radio person that does L-band moon bounce with dishes could do this, but finding a 1' dish that's the right size/shape and portable is another question.