It depends on a number of factors.
The aerial wall plates could be wired back to some sort of splitter device which feeds the TV aerial to the various rooms. So all wall plates would be outputs of that splitter and probably have no signal path between them for the magic eye signals.
So simply plugging in the Sky box at one plate and the magic eye at the other is very unlikely to work. Not to mention the RF signal from the Sky box probably won't get through either, or be unwatchable if it does.
How you get round this depends on whether you have an aerial on the roof or in the loft that is used to provide Freeview round the house. If so do you want to retain this? And also just what, if any, splitter device is used wherever all the cables come together.
If you have an aerial and want to keep it then that could involve running another length of coax cable from the aerial down to the living room. This then goes to the RF in on the Sky box. You then replug the existing living room feed from the output of the splitter to the aerial IN on the splitter. And finally plug a lead from the RF 2 out (on older boxes or just the RF out on the optional dongle newer boxes use) to the wall plate.
This will then feed the aerial and the output of the Sky box to all the other TVs. If the splitter device is the correct type it may also pass the magic eye signals as well. If not it may need some sort of bypass kit to feed these signals to the appropriate room feed. Or change the splitter to one that is compatible with magic eye devices.
If you don't want the TV aerial feed life is a bit simpler. You just locate the two room feeds and plug them together directly, might need a coupler to achieve this. So in effect you make a continuous cable run from living room to bedroom. Done right no reason why that shouldn't work.
Or you could just run a bit of coax directly from living room to bedroom, plug on end into the Sky box and the other via the magic eye into the bedroom TV and bypass all the internal distribution entirely. Though that is likely to be a less elegant solution and may not go down too well with the rest of the household...
But just plugging in, crossing your fingers and hoping most probably won't work