How to replace drywall adjacent to wall cabinets and then tile over it?
An untaped (unsupported) joint is an opportunity for more flex than you want in a tiled wall. I'd definitely try to bond the new and old drywall as well as possible. 

Unfortunately the best time to replace the drywall was while the cabinets were out, when you could have cut the drywall up above the lower cabinet line and buried it. Now, I'd probably either cut right at the top of the tile or try to remove a row of full tiles and come down a few inches lower. In either case you should be able to tape the joint with fiberglass mesh embedded in a skim coat of tile mortar. 

The alternative would be to put in framing blocking behind the entire top edge of the new drywall, or to use something more robust, such as cement board. Just don't leave it to floating drywall and the tile itself to prevent flex, and therefore cracked tile and grout.