Generally agree with the above - though it depends how springy the joists/floorboards are on which you are working. May be able to get away it if you use fully-flexible adhesive. Your tradesperson should be able to assess the situation and advise.
You'd have had some sort of a step anyway due to the thichness of the tiles. A wooden or metal edging strip set against the tiles at the door won't look out of place.
hello steve i am a tiler you need to put an overboarding down definatly not hardboard as the moisture in the adhesive will warp the boards should be 18mm ply but in order not create to much step a boarding called NO MORE PLY can be used at 6MM i highly recommend this product.most tile suppliers will either stock it or know where to purchase it it is easilly fitted to,