I guess from your description its an inset sink ie the correct sized hole was cut in the top, then the sink dropped in and sealed usually by a foam rubber seal under its lip, and a number of clips were tightened from underneath. I further assume you wish to replace the sink with a new one? First and most important hurdle is will new sink fit existing cutout? (ideal), will new sink require larger cutout (possible) or will new sink need smaller cutout (give up whole project at this point). But in answer to your original question, providing you can break the seal with the worktop (can't see any reason why this should be a problem) (you will need to be able to remove all the clips underneath) and the sizes of the old sink and new sink are in your favour - then yes carry on!
Alan R, December 2007