No it wouldn't improve the business case, as that factors in operational costs of, and demand on, all services, not just HS2.
You'd be adding operational cost (and extra fleet etc) to extend HS2 services for a diminishing return on how many more passengers would transfer to use it instead of conventional services, so the business case would actually worsen. Or, at best, HS2 would just be replacing a conventional service to carry the same passengers.
The proposed train service is designed to place HS2 trains where utilisation of the service would be greatest...but there gets a point where adding more bits on doesn't generate sufficient benefits any more to offset the extra cost etc of doing so.
For example, serving Edinburgh via both the WCML and ECML would split London demand via both routes, but you'd be adding operational cost to HS2 services to carry passengers between (for example) Newcastle and Edinburgh who would be catered for in exactly the same way by existing services.
Indeed, part of the business case is that although the trains are longer and way more seats than for many routes (Manchester benefiting the most from this) the actual number of extra coaches will be fairly limited.
In fact in the case of Manchester, depending on how many 11 coach services currently run HS2 may actually reduce the number of coaches needed.
Current 9 coach at 3tph and going end to end and back in 5 hours requires 135 coaches.
HS2 services with 16 coaches at 3tph and going end to end and back in 3 hours requires 144 coaches.
As such if 5 of the 15 units needed are 11 coach trains then the number of coaches increases to 145.
However that's only looking at current services, many suggest that we should go to 12 coach trains in the future to cater for demand. If that were to happen then there'll be a need for 180 coaches.
As such the leasing costs will be higher (even if the lease costs for HS2 trains were, say, 15% higher), however you also need more staff to run the same frequency of services. Which further adds to the costs.
Then there's not the same potential for passenger numbers, as even a 12 coach 80x (and they would be longer than a 12 coach 390) would only have ~800 seats compared to HS2 services which are cited as having 1,100 seats.
That's before you start to get people using rail more as the journey times are much smaller.