My very rough understanding is that HS2 as of phase 1 is that it is merely redirecting the long distance non stop down HS2 instead of the southern WCML, replacing the Pendolinos with the 895s. So effectively, North of Birmingham the WCML will work just the same as today.
Train length will be an issue.
HS2 trains are (unless the spec is changed) 200m, or 400m doubled up, and 200m is mostly too short for the capacity needed on the WCML.
The WCML is not generally sized for 400m trains, but there are platforms at Crewe (P6 towards London and P12 in both directions) which are longer than 400m.
Carlisle P4 is 390m so might be able to handle HS2 trains with a short extension.
Otherwise physical changes will be needed with resignalling which will be expensive.
There is currently no route from Crewe P6 (full length) or P12 towards Manchester.
HS2 400m trains could split in those locations into 2x200m to complete their journeys.
Splitting trains at Birmingham Interchange might also be possible to avoid WCML changes.
But all this seems inadequate for major flows like London-Manchester/Liverpool/Glasgow, and splitting/joining long-distance trains is a fraught business at the best of times.
The best answer would be to revise some of the HS2 formations to form something like the 266m of the current 11-car Pendolinos.
Or upgrade the on-board signalling on the 390s for ETCS and allow them to operate on HS2.
The displaced 200m HS2 sets could then be deployed on classic lines that don't need longer trains.