HS2 will cater for some existing Crosscountry service demand, but makes no difference on many existing journeys in/out/through Birmingham. There will be a similar situation at other points where it meets the HS2 network. Crosscountry acts as the principle express service along many of its corridors, and significant locations along these corridors will not gain a HS2 service to other not significantly far away significant locations.
I would think, that with regards to the existing Manchester, Edinburgh, Plymouth and Bournemouth network, the regular service should at least run through to a point on the West Coast Mainline, Doncaster, Taunton and Basingstoke which, post HS2, could all potentially have frequent express services to significant end locations of interest. I think that there should be at least an every 30 minutes Crosscountry service to these nodes to provide connectivity (although parts of services could be transferred to other operators if better overall, if TOCs as we know them still exist at this future point in time). I do not think there will be a need to run via the Leeds detour since this demand can be effectively served by HS2, frequent Midland Mainline services between Leeds and London or Nottingham, and Transpennine Express.
The setup of the Crosscountry service pattern beyond the West Coast Mainline connection, Doncaster, Taunton and Basingstoke will need to be determined considering, or in conjunction with, the connecting services on those main lines, in order to create the optimum compromise between costs and journey opportunities for passengers.