The answer appears to be a yes. But we need more information about your phone. Exact model number, carrier, CDMA or GSM, etc. The more specific you can be about the phone you have the better.
Typically the process for getting Android on a WinMo phone is this, unlock with a custom bootloader, install a newer radio (not always required, depends), install a custom ROM, and then install Android using your preferred method. You mileage will vary as the process for installing a custom ROM differs for each phone manufacturer.
There are 2 main methods. 1 install HBOOT and run Android from the SD card and memory. This is preferred by me and many others because it doesn't disrupt the actual phone itself, rather it runs on top of your WinMo phone. This means you can keep your WinMo phone in tact and can easily go back to it any time.
2 flash Android ROM over WinMo and go full Android. This method is more risky because you are flashing a completely different OS over whatever WinMo ROM you had installed. So there is no easy way to go back to WinMo. You would have to flash a WinMo ROM and start over to go back to it. This method is a more permanent Android running on a WinMo phone solution.
I would recommend the 1st method first. Then go from there. But personally I never flashed Android on a WinMo phone. The other method was way too convenient for me.
I have some links below that should help, but your version of your phone is going to be key. DO NOT start downloading files and running them until you understand that your phone version is supported by the tools you are using.
http://forum.ppcgeeks.com/showthread.php?t=103190&highlight=install+custom+rom
http://www.modaco.com/content/i9x0-omnia-http-omnia-modaco-com/289028/project-andromnia-android-on-omnia/
http://andromnia.net/
It looks likes the i900 and i910 are well supported, so if you have one of those you should be good to go.