Given alot of the Manchester - Heathrow traffic is connecting traffic, I'm not sure that will be appreciated.
I've flown MAN-LHR or back 189 times in the last decade, most of that connecting to BA from Terminal 5. That just about works on the way out when I lived in Hale Barns -- 30 minutes from sofa to plane, 60 minutes to T5, then 60 minute minimum connection. However that relies on high frequencies. I've been sat in a lonely T5 F lounge waiting 90 minutes+ for the flight to Manchester to even start boarding.
Knowing I could have exited, hopped on a Heathrow Express, and within 60 minutes of leaving passport control be on a train with less than an hour to go is far better, and this assumes you're living near Airport or getting a taxi from there. Live nearer Crewe, Warrington, Wigan and HS2 wins far more.
As for customs - Manchester is far worse than Heathrow. If you have something to declare, having to do that at Manchester on arrivals is a major pain (it's a pain at heathrow as they don't care, but you're more likely to get sorted in half an hour or so in my experience)
To flights from T2/3/4, forget it.
From Hale Barns HS2 station it will be 90 mintues to T5 and planning to arrive an hour before takeoff, so same time if the flight connection is perfect, but on average your connection will be 2 hours, HS2 frequency makes it faster.
Setting aside T5, going to T2/3/4 it will be better to get the train, and there will be a train every 20 minutes rather than a plane every 2 hours, and no need for 2 lots of security.
When we flew to Singapore/Sydney with 18 pieces of checked baggage, sure, flying from Manchester was great - the only other option would be driving to Heathrow (or flying direct from Manchester to Singapore). But for the other 187 times I did that route, HS2 would be just as good if not better.
(Now I live in South Cheshire, I drive to Heathrow rather than going to Manchester and flying, which is bad for tier points, but good for time and flexibility)