I was on the Dream 2 weeks ago and mentioned to our room host that it was missing and wanted one to be put in the room. He told me that all of them were removed because the docking stations were not compatible with new phones. He didn't know when they would be replaced but at the time there were no room clocks available.
I was on the Fantasy last month and noticed that the clocks were gone from the rooms. They used to have the digital clocks that were very bright, as someone else noted in this thread. The explanation given above seems to me to be nonsense: so what if the connector was the old 30-pin Apple connector and not compatible with newer iPhones - either type of connector is not compatible with any non-Apple device, and there's still the primary function of the alarm clock being, well, a clock that tells the time and functions as an alarm. IMHO, either that explanation is one of those "Disney lies" that they like to tell when they don't want to say what the real reason is, or it's something that the stateroom host just made up on their own.
I wonder if my clock that sets time automatically will work.
If it's relying on a satellite signal, probably not. It would probably, if it did anything at all, try to set to whatever the "local" time is where it's located at the moment. And that may or may not be either ship's time or port time. It's best to have a basic clock that you set the time.
I'm not aware of any kind of clock that relies on a "satellite signal" to set itself, other than something that's based on GPS. Mobile phones that set their own time rely on the "time service" signal from the cellular provider, which is optional. The Cellular At Sea cellular service on board does not advertise a time, so your phone won't change time zones with the ship even if you have the phone on and not in airplane mode. A mobile phone may change time zones if it's not in airplane mode, locks onto a nearby land-based signal, and that provider advertises time service, but that time will be based on whatever the local time is at that land location, which may or may not be the same as the ship's time (usually it is).
Almost all stand-alone clocks that are sold in the US that can set themselves, whether they be plug-in or battery operated, rely on a terrestrial radio signal that the US government broadcasts from two locations: Colorado and Hawaii. The Colorado transmitter covers the entire continental US, and as such, cannot provide the notion of "local time" as the transmitter does not know what time zone the clock is in. So, such clocks rely on the user to configure what time zone they're in. So, if you had such a clock on board, and assuming it could receive the signal from Colorado, it would provide very precise minutes and seconds, but as to what hour it was, would still rely on the user to configure that manually.