If you are buying the unit new I think this should work tip-top....
I checked inside the box of a fairly posh sony headunit (before some of the low end tat!) that we are putting in an Elan shortly and iirc the unit came supplied with an adaptor loom which allows you to connect to the cars (omega) standard loom but CRUCIALLY addresses the problem of the 12V supplies being switched by fitting a couple of bullet connectors inline with the relevant supplies (blue and yellow?).
Don't quote me on that but what i'm long-windedly trying to say is that YES, it should work fine. I can't confirm the sony will feed the radio display like your standard radio though? If it doesn't, it will simply display date. The h/u cage will also be supplied and will be required. Biggest problem I believe is that even though the omega is a big car, space behind the stereo is rather tight so may take some fiddling.
Don't get stuck, pop back on here and we'll help you through it....and make sure the radio you choose has some anti-theft features about it! Oh, and if the munkehs at halfrauds can fit it then so can you! Shouldn't take more than 1-2 hrs