Roland Perry wrote:

HEx amd a £230m contribution towards Crossrail, and are letting
Crossrail use "their" platforms and access vis airport junction. I
would not find it surprising if some concessions went in the other
direction (and they'd be paying Crossrail track access charges too).

I'd also found this article:

24 March 2011

Airport operator BAA chief executive Colin Matthews this week
threw his weight behind plans to run Heathrow Express services
through Crossrail’s central London tunnels.

He said he was backing the idea of extending the dedicated
Heathrow services east from their current Paddington terminus
and into the tunnels being constructed for Crossrail, "with
maximum enthusiasm".

The plan was outlined by Network Rail in its London and the
South East route utilisation study late last year.
Network Rail believes this would also remove the need for many
passengers travelling between Heathrow and central London to
change trains at Paddington.

BAA had previously campaigned against calls to dovetail
Heathrow Express with Crossrail. It objected to the
legislation that authorised the line, fearing that the
Department for Transport could take over the Express service.

However, Matthews told a Westminster Energy, Environment &
Transport Forum event last week that BAA now backs the idea.

"The opportunity of Heathrow Express going forward with
Crossrail, to make sure you can get from Heathrow not just to
Paddington but to other destinations in London, is going to be
great," he said.

Having read the 2011 RUS, it does not propose that Heathrow Express
trains would run onto Crossrail. In fact it proposes the opposite, that
Crossrail would replace HEx, running up to 10tph on the Relief Lines to
Heathrow T4 or T5, skip-stopping to reduce journey times.

Peter Smyth