Just read the review for the first time. The Pullman is walkable from T2 as I have done it, I was on a road for part of the journey so not recommended. If the hotel bus is not due you can catch the Terminal transfer bus, both depart from the departures drop off area upstairs. I have been a frequent guest at the neighbouring Novotel and it’s a good alternative, also has a lounge, I suspect both hotels were built together and are the same quality in terms of soundproofing!