I won't shoot you but they would serve different markets.
The locals and XC would be for local markets, whereas the HS2 link would be for passengers from Birmingham and Manchester, the latter removing domestic if the services are well implemented (with check in available at HS2 stations, and checked luggage carried on the trains in a goods wagon, and then taken by baggage handlers throughout the airport, and have it integrated fully with baggage systems at both ends)
So as a passenger would see it...
BA Check In at Rail Terminal at Manchester, checked all the way to their final destination, eg JFK.
Walk off the train an hour later at Heathrow Rail, on a few moving walkways though transfer security (that exists anyway) and into Terminal 5.
Baggage is loaded onto high speed luggage belts linked into T5 and the CTA, possibly onto T4 aswell, but it would need looking into, theres already plans for a high speed belt between T3 (For the CTA) and T5.
Personally, I'd also like to see HS2 continue and terminate at Gatwick, not nesseserally at HSRail speeds, but within 20 - 30mins journey time, and have services terminate at Gatwick rather than Heathrow, providing ?4tph between the two airports, again, linked in with baggage systems for flight transfers.
And in relation to bi-modes in T5, T4 and CTA stations, the engines will be off, not idle...