While I don't subscribe to GP's view that satellites have bandwidth for "video recording the entire planet at all times", it seems plausible that SIGINT satellites would have a relatively constant bandwidth available for observation. As a (non-geostationary) satellite passes over relatively unpopulated areas (e.g., the southern Indian Ocean), it will be "bored" and thus far more likely to notice a single low-power transmission.
On the other hand, if it is storage and downlink bandwidth that is limited, sats would probably be programmed to ignore or discard uninteresting signals. This seems likely to me.
So the question may be whether commercial airliner pings from the southern Indian Ocean area were considered 'interesting' at the time and, if not, did anyone realize there was a rogue 777 in time to re-task the satellites?
Regardless, I'd bet those signals are considered interesting going forward.
The other complication is that Inmarsat up-link is a steered spot-beam ( the antenna on the aircraft is stabilsed and driven, or phased-array in recent implemenations ). So the SIGINT sat would have to be passing through the up-link 'beam' precisely as it was transmitting.
Down-links are ( depending on generation and usage ) either from one of an array of narrow-beam antennae on the Inmarsat or from the wide-area general broadast antenna; much easier to intercept, you and I can do it with a sat-TV dish and an RTL dongle.
Brochures I saw years ago indicated that least some portable Inmarsat terminals are also directed beams. Taliban/AQ was known to use directional antennas for communications security, at least later in the war. So possibly we could say the same thing about Bin Laden's satphone, and we know how that turned out.
On the other hand, if it is storage and downlink bandwidth that is limited, sats would probably be programmed to ignore or discard uninteresting signals. This seems likely to me.
So the question may be whether commercial airliner pings from the southern Indian Ocean area were considered 'interesting' at the time and, if not, did anyone realize there was a rogue 777 in time to re-task the satellites?
Regardless, I'd bet those signals are considered interesting going forward.