The whole idea is that services would stop - existing stopping services, increased in frequency depending on infrastructure improvements and HS2's effect on London-Birmingham traffic via Chiltern, would use the Dudding Hill Line to terminate at OOC instead of Marylebone.
It would still require investment but no tunnelling would be required, no work needed to allow for 10 car EMU's (which would likely be overkill anyway), and crucially the benefits of a direct link to the HS2/GWML/HEx/Crossrail/NLL hub at OOC would be extended to Northolt, Sudbury, Wembley and Harlesden too.
I must confess, it looks far longer on a map than it is in actuality, but it is still quite the diversion. The way I see it though is that the Chiltern Birmingham services aren't end-to-end expresses - they generally serve Birmingham to Banbury
then become expresses to London. This demand isn't going to be alleviated by HS2, and it can't be by improved WCML services, so the Chiltern services will have to do so. Four tracking Northolt Junction-High Wycombe would enable a segregated Crossrail service to operate (though still feasible with two tracks and lots of loops I suspect), leaving the remaining "mainline" and outer suburban services (Oxford/Bicester/Banbury/Birmingham) free to run into Marylebone without conflict. I suspect in time though, the Oxford and Bicester services woudl end up on Crossrail, much like Reading probably will be. This could work well - the Chiltern route would be even more attractive to passengers if they still ended up at Paddington.
You also have to consider the stations on the Northolt Junction-Neasden Junction section in context - they all have terrible service and have alternatives nearby with much higher service levels, and they sit on a congested two-track line. Even rebuilding the platform loops would only get you so far - there's a decent argument for closing them. Alternatively, four-tracking the line then serving it with a branch of the Jubilee from Neasden could be possible, but it still doesn't avoid the situation they all have alternatives nearby.
...but going back to the tunnelling, the TBM is going to be tunnelling from West Ruislip station to Northolt Junction at the very least as of last January, and hopefully
Ealing's pressure to get the tunnel extended will prevent HS2 cutting corners.