The only things that should be 'happening in the north' while HS2 is being built between Birmingham and London are the beginnings of infersturcture needed for HS2.
For example, in Manchester.
Work should be started on the terminus in Manchester City Centre, (IMO, Mayfeild & Barring St Industrial area gets flattened and built up as the terminus, possibly using the Facade of Mayfeild, linked in with moving walkways etc into Piccadilly with a new high level concourse connecting over Fairfeild St with the HS2 station, Platforms 13 - 16, the glass face onto Fairfeild St (Where one of way too many costa coffees is, next to Pt 12, providing a much wider link to Pt 13 - 16, improved access from further down Fairfeild St, modifications to the A635 to provide vehicle access, and provision for extention of the A635 as a D2AP road to meet the A57/M67 further out.
Outside of the station, widening the viaduct approaches to 10/8 track, segregating each traffic set on the approach to Piccadilly / Mayfeild into
HS2 U&D, Airport U&D, Stockport Slow U&D, Stockport Fast U&D, East Manchester U&D
As a tempoary measure, the HS2 lines would join in (possibly grade seperated, possibly not) with the fast lines at Longsight (where it would be sensible to send the HS2 lines into a tunnel).
Then work in the Manchester Area can begin on tunneling out to Sale Water Park and co-operation with Metrolink to share the alignment through Wythenshawe to meet up with Manchester Airport (North of the M56 Spur), with the though lines also initally following this route, or turning a sharp bend and following the Stockport - Altham alignment and heading off to cross the ship canal on the old embankments, new bridge and new D2M/D3M combined road bridge over the ship canal and mersey. Kind of like a big spread out delta junction.
When on the other side, Manchester West Parkway would be built at J11 on the M62 mainly for P&R and Northbound connections, then linked into that Chat Moss Line for Liverpool via St Helens and WCML for onward connections to Preston & Glasgow.
Some parts of this project are utterly massive, and some of the assets, such as the alignment into Manchester (if it can be linked into an existing line temporaraly) since almost all approaches are at capacity, the HS2 station would cirtanly come in handy as it would allow 400m services to run from Day 1 in the peaks.
And if the approaches where joined up on the approaches into Manchester and a temp link put into the Styal branch or near Cheadle Hume, with Manchester S and Manchester W Parkways provided, HS Commuter services could begin as soon as they where completed.
Then to join Manchester into the HS2 network as a whole, just join the dots from Rugley to Ringway.
So yes, some work should be done up north early on, but it shouldn't detract from the major works in London being done first.