John, I have a SPOT 1 and a SPOT 2. #1 was idle until yesterday when I re-activated it -- I've loaned it to a northbound JMT hiker. And my #2 will be loaned to a southbound hiker later this month. Pretty cool that they will probably meet, and I'll be watching!

As for the Spot Connect, I don't have one, but I'd assume the Android phone is only required for the text entry. No way it would need to be connected to a cellular system -- that would make the other device much less useful. But yes the phone would need to be operational in that it could accept text input, and pass it via the Bluetooth link to the SPOT unit. It would be a foolish hiker to leave the phone on and drain its power while in the backcountry.
As for unstable: They are quite stable in my opinion. One just needs to understand their limitations: They need to be able to lock onto GPS satellites to gain your location. So being in a valley with steep/high sides could be a problem. Also, under trees, they can lose their location. Today, we were playing with Spot 1, and it lost location because we were standing near and overhanging roof, with half the sky visible. Ten feet away would have been fine.
Second part, the SPOT needs access to the satellites receiving its signals. That has several limitations: First, there are periods when there is no satellite in view. Second, the SPOT MUST be placed face up. I carry mine attached to the shoulder strap of my pack, right on top of my shoulder. And then, when in Sierra forest cover, many times the signals don't get out.
To compensate for the problems below the forest canopy, and where no satellite is available, the units transmit a signal every 5 minutes. A common mistake some people make is to turn on the SPOT, send an OK signal, then turn it off within 10 minutes. The unit has only transmitted once, so if no satellite was above, no signal got out.
I'm not sure about the receiving satellite needing to also be connected to a ground station. But then, in the Sierra, I am sure the satellites are in contact.
It has been my experience that no messages are delayed. Either they make it right away to the SPOT site, or they never do.
Regarding
InReach from DeLorme: it costs $250, and the DeLorme Earthmate
PN-60W GPS unit is $350. LL Bean doesn't report what a subscription for the satellite service costs. Do you know?