FWIW, assuming the tiles are ceramic, I would use a self levelling compound to give a smooth finish, then put the floor covering over that.
Similarly, if there is a patch of floor without tiles, you can get some high build floor leveller (max c15mm I think).
Of course by the time you've done that and added carpet and underlay, you're probably up 1" on your starting floor level. Not necessarily a problem, as long as you can live with an odd door bar. In our last place, we put reclaimed pine boards down on a concrete floor, which took us up about 1". I graded this out over 2-3" by planing and sanding the first board in the doorway and when it was done it wasn't noticeable.
Personally I wouldn't bother lifting the floor - did it in an old house and, as said it was messy and an unpleasant job.