It depends on how you define 'Heathrow'. For BA passengers, it would definitely be one change away, but for some of the others it would be two, even three for Terminal 4. You can probably get away with that, since BA tends to have much more of a UK passenger base (being the national carrier) who would be more likely to arrive from the west than foreign passengers. However, it would surely be much better to access Heathrow Central, and that means mixing with HEX.
If we do end up with more than one route in, but only one requires premium fares, then clever individuals like some of the people here will soon spot something. If you go to Slough and then catch a Reading-Heathrow service back, you miss the premium fares completely. That plus the shift to Crossrail for direct trains would effectively torpedo HEX except for those in a real hurry, meaining either a frequency cut or the end of the premium fares to get passengers back.
The complication of multiple stations for Heathrow's terminals (compared to Manchester, which has just one station to cover its three terminals) certainly adds to the mix, true!
The way I'm thinking is that if you extend the current HEX services westwards then they cease to become "premium" (esp if you can use the normal London - Slough fare on the HEX service to get to Slough, but have to pay a significantly higher fare just to do London - Heathrow).
But, if you run a lot of non-stop Paddington - Heathrow services (which extend to Bristol/ Oxford/ Wherever) with normal fares then you partly undermine the case for Crossrail and are using up "overground" platform space at Paddington for Heathrow services at the same that a large number of Crossrail services from the east are terminating at Paddington.
But if you extend more Crossrail services to Heathrow then you either force all London - Heathrow passengers to use an "all stops" service, or you complicate the simplicity of Crossrail stopping everywhere.
Plus, whilst Crossrail could be extended *beyond* Heathrow, its a long way to go on a toiletless train (and certainly no chance of it running west of Reading).
I think the only way of doing it would be to keep the western Heathrow service separate from the eastern Heathrow services (so that it's not affected by whatever happens to Crossrail/ HEX) and run it no further than Oxford/ Basingstoke (so that its not disrupting the Bristol/ Cardiff passengers - they can simply change at Reading).
Unless, of course, the Old Oak Common idea for HS2 becomes an acceptable place to change from all main line services to a Heathrow shuttle, in which case all the millions spent on a western link into Heathrow are a waste!