Why not? There are thresholds for differing floor heights. Wood to carpet. Tile to wood, whatever. If you want a perfectly flat transition, ie. no threshold; then just put down 1/2" osb underlayment and lay the hardwood.
This !If the tile is higher use bull nose edging pieces
Another posibility if you have 12 feet of floor space running out into your living room from the tile edge would be to put a 1-1/2 wide x 1/2" furring strip at the tile. Then every 16 inches put down a 7/16, then a 3/8, then a 5/16, then a 1/4, then a 3/16, then a 1/8, then a 1/16 inch furring strip. I really don't think you will see the slope @ 1/16" per 16 inches.
I have almost exactly the same situation at my house. I made my own oak transition piece, 3-1/2 inches wide, 3/4 inch thick, back cut with a 3/4 inch wide, 1/2 inch deep dado to cover the tile. I cut a 30 degree bevel on the front of the transition piece, works fine, no trip problem, looks good. Or you can buy a standard transition piece from Bruce or another company that can accommodate most any transition height.